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We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kähler metric for every Kähler class. We show that there are only two such rational surfaces, namely the projective plane and the quadric surface. In particular, we show that all rational surfaces other than those two admit a destabilising slope test configuration for some polarisation, as introduced by Ross and Thomas. We further show that all Hirzebruch surfaces other than the quadric surface and all rational surfaces with Picard rank 3 do not admit a constant scalar curvature Kähler metric in any Kähler class. [ABSTRACT FROM AUTHOR]

An analytic dielectric introspection in two cardinal ferric oxide polymorphs, viz. hematite and maghemite, is conducted using a three-fold line of direction. Firstly, dc field-dependent radio/audio-frequency impedance and dielectric spectra of polycrystalline MIM pellets, comprising near-stoichiometric (meticulously characterized) Fe2O3 nanoparticles, are analysed by employing the Cole–Davidson model, Jonscher's power law and equivalent circuitry to quantify non-Debye dipolar relaxations, small polaron hopping conduction, grain core–boundary resistivity correlations and field-driven delocalization/de-trapping of carriers. Bias-tuned low-frequency enhancement of the dielectric constant by augmenting Maxwell–Wagner polarization is demonstrated for both samples, a prerequisite for conquering classical energy-storage bottleneck. Secondly, the optical dielectric function and associated parameters are evaluated under a density functional theory + U framework, to physically designate particular resonant absorption, dissipation, electronic polarization and decay. In doing so, a new crystallographically consistent and energetically stable vacancy-ordered maghemite-type supercell is constructed to accomplish reasonable computational cost. Thirdly, intrinsic anisotropy in materials sensitive to photonic excitations is videographed by simulating energy-dispersive evolution of the quadric surface to project real/imaginary dielectric tensors. The authors anticipate that this intensive technique will pictorially demonstrate anisotropic deviations in the dielectric ellipsoid, fostering materials physics over linear and nonlinear dielectrics. [ABSTRACT FROM AUTHOR]

Let S be a set of n points in real four-dimensional space, no four coplanar and spanning the whole space. We prove that if the number of solids incident with exactly four points of S is less than K n 3 for some K = o (n 1 / 7) then, for n sufficiently large, all but at most O(K) points of S are contained in the intersection of five linearly independent quadrics. Conversely, we prove that there are finite subgroups of size n of an elliptic curve that span less than n 3 / 6 solids containing exactly four points of S . [ABSTRACT FROM AUTHOR]

A rotary laser optoelectronic measurement system is used as part of a multistation network for large-scale metrology. The line-structured laser surface of the transmitter is regarded as an ideal plane for the intersecting measurement. This article presents how the rotary laser surface model can be optimized for large-scale optoelectronic measurement systems. Initially, the deformation of the laser surface caused by the assembly error in a cylindrical lens is analyzed by Zemax simulation and studied by a visual evaluation method based on a high-precision triaxis rotary table. Based on the analysis result, the folded linear surface model and the quadric surface model are applied to reestablish the laser surface model, respectively, to reduce the shape error. A high-precision 3-D coordinate field is designed to acquire an accurate surface parametric model and validate the fitness of the new models. The experimental results based on workshop measurement positioning system (wMPS) show that both optimization models are conducive to improving the fitting accuracy of laser surfaces, and the quadric surface model fits better when the surface shape is closer to the commonest two-folded linear model. Finally, optimizing the laser surface model plays an important role in improving the system measurement accuracy. [ABSTRACT FROM AUTHOR]

The intersection of surfaces in n-dimensional space F will form the integral curves that are the solutions of the partial differential equations whether dimensional or non-dimensional, and if the integral solutions are closed curves, then they form the Archimedean solids that would not necessarily have symmetric surfaces enclosing the feasible region and that not necessarily follow the Lipschitz condition. [ABSTRACT FROM AUTHOR]

A tensor product surface S is an algebraic surface that is defined as the closure of the image of a rational map φ from P1 × P1 to P3. We provide new determinantal representations of S under the assumptions that φ is generically injective and its base points are finitely many and locally complete intersections. These determinantal representations are matrices that are built from the coefficients of linear relations (syzygies) and quadratic relations of the bihomogeneous polynomials defining φ. Our approach relies on a formalization and generalization of the method of moving quadrics introduced and studied by David Cox and his co-authors. [ABSTRACT FROM AUTHOR]

Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and pro-jective geometry, we address new questions motivated by algebraic statistics and optimization. We compute the reciprocal curve and the maximum likelihood degrees, and we study strata of pencils in the Grassmannian. [ABSTRACT FROM AUTHOR]

We study the reciprocal variety to the LSSM of catalecticant matrices associated with ternary quartics. With numerical tools, we obtain 85 to be its degree and 36 to be the ML-degree of the LSSM. We provide a geometric explanation to why equality between these two invariants is not reached, as opposed to the case of binary forms, by describing the intersection of the reciprocal variety and the orthogonal of the LSSM in the rank loci. Moreover, we prove that only the rank-1 locus, namely the Veronese surface v4(ℙ²), contributes to the degree of the reciprocal variety. [ABSTRACT FROM AUTHOR]

We examine quadratic surfaces in 3-space that are tangent to nine given figures. These figures can be points, lines, planes or quadrics. The numbers of tangent quadrics were determined by Hermann Schubert in 1879. We study the associated systems of polynomial equations, also in the space of complete quadrics, and we solve them using certified numerical methods. Our aim is to show that Schubert's problems are fully real. [ABSTRACT FROM AUTHOR]

The Zariski closure of the central path which interior point algorithms track in convex optimization problems such as linear, quadratic, and semi-definite programs is an algebraic curve. The degree of this curve has been studied in relation to the complexity of these interior point algorithms, and for linear programs it was computed by De Loera, Sturmfels, and Vinzant in 2012. We show that the degree of the central curve for generic semidefinite programs is equal to the maximum likelihood degree of linear concentration models. New results from the intersection theory of the space of complete quadrics imply that this is a polynomial in the size of semidefinite matrices with degree equal to the number of constraints. Besides its degree we explore the arithmetic genus of the same curve. We also compute the degree of the central curve for generic linear programs with different techniques which extend to bounding the same degree for generic quadratic programs. [ABSTRACT FROM AUTHOR]

To any homogeneous polynomial h we naturally associate a variety Q.h which maps birationally onto the graph ⌈h of the gradient map ∇h and which agrees with the space of complete quadrics when h is the determinant of the generic symmetric matrix. We give a sufficient criterion for Ωh being smooth which applies for example when h is an elementary symmetric polynomial. In this case Ωh is a smooth toric variety associated to a certain generalized permutohedron. We also give examples when Ωh is not smooth. [ABSTRACT FROM AUTHOR]

Sphere tracing is a common raytracing technique used for rendering implicit surfaces defined by a signed distance function (SDF). However, these distance functions are often expensive to compute, prohibiting several real-time applications despite recent efforts to accelerate them. This paper presents quadric tracing, a method to precompute an augmented distance field that significantly accelerates rendering. This novel method supports two configurations: (i) accelerating raytracing without losing precision, so the original SDF is still needed; (ii) entirely replacing the SDF and tracing an interpolated surface. Quadric tracing can offer 20% to 100% speedup in rendering static scenes and thereby amortizes the slowdown caused by the complexity of the geometry. [ABSTRACT FROM AUTHOR]

• We propose the µ-basis formulas for the implicit monoid curves/surfaces. • New µ-basis formulas for the parametric monoid curves/surfaces in general expression. • Approximate µ-bases are computed for the monoid curves/surfaces as well as the error estimations. [Display omitted] The μ -basis is a developing algebraic tool to study the expressions of rational curves and surfaces. It can play a bridge role between the parametric forms and implicit forms and show some advantages in implicitization, inversion formulas and singularity computation. However, it is difficult and there are few works to compute the μ -basis from an implicit form. In this paper, we derive the explicit forms of μ -basis for implicit monoid curves and surfaces, including the conics and quadrics which are particular cases of these entities. Additionally, we also provide the explicit form of μ -basis for monoid curves and surfaces defined by any rational parametrization (not necessarily in standard proper form). Our technique is simply based on the linear coordinate transformation and standard forms of these curves and surfaces. As a practical application in numerical situation, if an exact multiple point can not be computed, we can consider the problem of computing "approximate μ -basis" as well as the error estimation. [ABSTRACT FROM AUTHOR]

From a block-diagonal (n + 1) × (m + 1) × (m + 1) tensor symmetric in the last two entries one obtains two varieties: an intersection of symmetric determinantal hypersurfaces X in n -dimensional projective space, and an intersection of quadrics C in m -dimensional projective space. Under mild technical assumptions, we characterize the accidental singularities of X in terms of C. We apply our methods to algebraic curves and show how to construct theta characteristics of certain canonical curves of genera 3, 4, and 5, generalizing a classical construction of Cayley. [ABSTRACT FROM AUTHOR]

Genus 5 curves can be hyperelliptic, trigonal, or non-hyperelliptic non-trigonal, whose model is a complete intersection of three quadrics in P 4. We present and explain algorithms we used to determine, up to isomorphism over F 2 , all genus 5 curves defined over F 2 , and we do that separately for each of the three mentioned types. We consider these curves in terms of isogeny classes over F 2 of their Jacobians or their Newton polygons, and for each of the three types, we compute the number of curves over F 2 weighted by the size of their F 2 -automorphism groups. [ABSTRACT FROM AUTHOR]

In this paper, we provide a construction of (q + 1) -ovoids of the hyperbolic quadric Q + (7 , q) , q an odd prime power, by glueing (q + 1) / 2 -ovoids of the elliptic quadric Q − (5 , q). This is possible by controlling some intersection properties of (putative) m -ovoids of elliptic quadrics. It eventually yields (q + 1) -ovoids of Q + (7 , q) not coming from a 1-system. Secondly, for certain values of q , we construct line spreads of PG (3 , q) that have as many secants to a given elliptic quadric as possible. This is then used to construct m -ovoids for m ∈ { 2 , 4 , 6 , 8 , 10 } in Q + (7 , 3). [ABSTRACT FROM AUTHOR]

Let Y be a smooth complete intersection of a quadric and a cubic in ℙn, with n even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, the Chow ring of (powers of) Y displays K3-like behavior. As a by-product of the argument, we also establish a multiplicative Chow–Künneth decomposition for the resolution of singularities of a general nodal cubic hypersurface of even dimension. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study Betti numbers of graded finitely generated modules over a quadratic complete intersection. In the case of codimension 1, we give a natural class of quadratic forms Q whose Clifford algebras are division rings, and deduce the possible Betti numbers of modules over the hypersurfaces Q = 0. Our approach leads to a new version of the Betti degree Conjecture. In higher codimensions, we obtain formulas for the Betti numbers in terms of the ranks of certain free modules in a higher matrix factorization. [ABSTRACT FROM AUTHOR]

For the optimization of anti-jamming agile waveform for helicopter borne fire control radar, an agile phase coding waveform suitable for multi-pulse and short code length is designed based on singular value decomposition (SVD) and cyclic algorithm. First, we construct the constrained quadric optimization problem with low sidelobe ambiguity function in the target region. Second, the quartic is transformed into the quadric according to SVD decomposition, and an iterative convergence algorithm is designed. Third, a quadric iterative convergence algorithm is deduced based on the cyclic algorithm. Finally, the simulation results show that the two algorithms are close to each other in the design of agile waveform optimization performance, but the SVD decomposition algorithm has faster convergence speed, and the cycle calculation algorithm has higher operation speed. [ABSTRACT FROM AUTHOR]

In this paper, we study real hypersurfaces in the complex quadric space Q m whose structure Jacobi operator commutes with their structure tensor field. When the normal vector field is A -principal we show that the Reeb curvature α is non-vanishing and determine principal curvatures of the hypersurface. In the case of A -isotropic normal vector field, we prove that the hypersurface is Hopf if it has vanishing Reeb curvature or commuting shape operator. We also consider Reeb flat hypersurfaces, namely when the Reeb curvature is zero. We see that this family of hypersurfaces is non-empty and among other results we prove that if the Ricci tensor of a Reeb flat Hopf hypersurfaces is Killing, then the Ricci tensor is parallel. [ABSTRACT FROM AUTHOR]

Analyzing the impacts of Cattaneo-Christov flux, bioconvective Raleigh number and cross diffusion effects in electrically conducting micropolar fluid through a paraboloid revolution is assessed in this work. Non-dimensional equations are solved numerically using shooting technique with an aid of Matlab software. The impact of various parameters on velocity, temperature and concentration are discussed in detail and presented graphically. Harman number and micro rotation parameters are found and have an increasing influence on shear stress. The vertical velocity increases at free stream and the horizontal velocity increases near the surface when Grb increases, which follows the opposite trend for accumulation of Rb. The numerical results are compared with the available data indicating good agreement in a limiting case. [ABSTRACT FROM AUTHOR]

This paper presents a meshless local Petrov–Galerkin method based on the particular solution (MLPG-PS) to solve a time-fractional inverse problem with unknown boundary condition. The particular solution obtained by using multiquadric radial basis function is used to construct basis function. First, we apply a finite difference method to discretize time-fractional derivative. Then, we use MLPG-PS method to approximate the spatial derivative. Since the coefficient matrix is ill-conditioned, the Tikhonov regularization technique is employed to solve the resulting system. Two numerical examples are tested to show the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we prove the irreducibility of the monodromy action on the anti‐invariant part of the vanishing cohomology on a double cover of a very general element in an ample hypersurface of a complex smooth projective variety branched at an ample divisor. As an application, we study dominant rational maps from a double cover of a very general surface S of degree⩾7 in P3 branched at a very general quadric surface to smooth projective surfaces Z. Our method combines the classification theory of algebraic surfaces, deformation theory, and Hodge theory. [ABSTRACT FROM AUTHOR]

We investigate the resolution of a general branched cover |$\alpha \colon C \to \mathbf{P}^1$| in its relative canonical embedding |$C \subset \mathbf{P} E$|⁠. We conjecture that the syzygy bundles appearing in the resolution are balanced for a general cover, provided that the genus is sufficiently large compared to the degree. We prove this for the Casnati–Ekedahl bundle, or bundle of quadrics   |$F$| —the 1st bundle appearing in the resolution of the ideal of the relative canonical embedding. Furthermore, we prove the conjecture for all syzygy bundles in the resolution when the genus satisfies |$g = 1 \mod d$|⁠. [ABSTRACT FROM AUTHOR]

We investigate the resolution of a general branched cover |$\alpha \colon C \to \mathbf{P}^1$| in its relative canonical embedding |$C \subset \mathbf{P} E$|⁠. We conjecture that the syzygy bundles appearing in the resolution are balanced for a general cover, provided that the genus is sufficiently large compared to the degree. We prove this for the Casnati–Ekedahl bundle, or bundle of quadrics   |$F$| —the 1st bundle appearing in the resolution of the ideal of the relative canonical embedding. Furthermore, we prove the conjecture for all syzygy bundles in the resolution when the genus satisfies |$g = 1 \mod d$|⁠. [ABSTRACT FROM AUTHOR]

On a real hypersurface M of a complex quadric we have an almost contact metric structure induced by the Kählerian structure of the ambient space. Therefore, on M we have the Levi-Civita connection ∇ and, for any non-null real number k, the so called kth generalized Tanaka Webster connection ∇ ^ (k) . We introduce the notions of ( ∇ ^ (k) , ∇) -Codazzi and ( ∇ ^ (k) , ∇) -Killing normal Jacobi operator on such a real hypersurface and classify Hopf real hypersurface in a complex quadric whose normal Jacobi operators satisfy any of both conditions. [ABSTRACT FROM AUTHOR]

In this paper we remove the solid incidence assumption in the characterization of J. Schillewaert (A characterization of quadrics by intersection numbers, Des. Codes Cryptogr., 47 (2008), 165–175) by proving that quadric plane incidence numbers imply quadric solid incidence numbers, except for the dual complete 11-cap of PG(4, 3). Furthermore, new characterizations of the parabolic quadric Q(4, q) and the ovoidal cone of PG(4, q) are provided. [ABSTRACT FROM AUTHOR]

We give a classification of real hypersurfaces in the complex hyperbolic quadric Qm∗=SO2,mo/SO2SOm that have constant mean curvature and harmonic curvature. [ABSTRACT FROM AUTHOR]

Based on discrete element method (DEM), three kinds of soil--rock mixture (SRM) models with diVerent coarse particle contentswere established and triaxial compression testswere carried out. The results show that the force chains in the particle system playing the main bearing role need more lateral supports, which results in the contact with a higher coordination number and often bear larger contact force. The relationship between the contact's carrying capacity and the coordination number can be fit by a quadric surface. Taking the fit quadric surface as the capacity function, the network-flow model of force transfer can be constructed to quantify the force transfer ability of a contact network. By connecting the maximum flow in the network with the hardening parameter of the unified hardening model, the stress--strain relationship of SRM can be predicted to some extent, which lays a basis for formulating micro--macro constitutive model for granularmaterials. [ABSTRACT FROM AUTHOR]

Three-dimensional analytical geometry is important in multivariate calculus courses, but students have difficulty learning it. We present results from a research on learning quadric surfaces by means of a didactical intervention based on the 3-dimensional dynamic educational software GAnalitica3D. We analyze the influence of the constructivist and collaborative nature of teaching and the visualization skills necessary to interact with the software. The experimentation was carried out with university students, who solved the problems in small groups and then made whole group discussions. We report on the assessment of students' initial knowledge carried out and present examples of solutions in which the progress and difficulties of students are demonstrated. We conclude that the software allows students to comprehensively relate the algebraic and visual representations of quadric surfaces, which facilitates their learning. [ABSTRACT FROM AUTHOR]

We develop a new technique to study ranks of multiplication maps for linear series via limit linear series and degenerations to chains of elliptic curves. We prove an elementary criterion and apply it to proving cases of the Maximal Rank Conjecture. We give a new proof of the case of quadrics, and also treat several families in the case of cubics. Our proofs do not require restrictions on direction of approach, so we recover new information on the locus in the moduli space of curves on which the maximal rank condition fails. [ABSTRACT FROM AUTHOR]

We develop a version of Ekedahl's geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros. [ABSTRACT FROM AUTHOR]

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article introduces a fast meshless algorithm for the numerical solution nonlinear partial differential equations (PDE) by Radial Basis Functions (RBFs) approximation connected with the Total Variation (TV)-based minimization functional and to show its application to image denoising containing multiplicative noise. These capabilities used within the proposed algorithm have not only the quality of image denoising, edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images. It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure. The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), and structural similarity index (SSIM) corresponded to the current conventional TV-based schemes. [ABSTRACT FROM AUTHOR]

We prove that the number of Legendrian rational cubics in ℂP3 through three generic points and a line is three. Also, we classify all Legendrian curves on a quadric surface. Additionally, several computations are verified using Macaulay2 computer algebra system. [ABSTRACT FROM AUTHOR]

We propose a discretization of classical confocal coordinates. It is based on a novel characterization thereof as factorizable orthogonal coordinate systems. Our geometric discretization leads to factorizable discrete nets with a novel discrete analog of the orthogonality property. A discrete confocal coordinate system may be constructed geometrically via polarity with respect to a sequence of classical confocal quadrics. Various sequences correspond to various discrete parametrizations. The coordinate functions of discrete confocal quadrics are computed explicitly. The theory is illustrated with a variety of examples in two and three dimensions. These include confocal coordinate systems parametrized in terms of Jacobi elliptic functions. Connections with incircular nets and a generalized Euler–Poisson–Darboux system are established. [ABSTRACT FROM AUTHOR]

In this paper we deal with compactifications of affine homology 3-cells into quadric fibrations such that the boundary divisors contain fibers. We show that all such affine homology 3-cells are isomorphic to the affine 3-space A 3. Moreover, we show that all such compactifications can be connected by explicit elementary links preserving A 3 to the projective 3-space P 3. [ABSTRACT FROM AUTHOR]

We construct potentially new manifolds homeomorphic but not diffeomorphic to CP 2 # 8 CP 2 ¯ and CP 2 # 9 CP 2 ¯ via rational blowdown surgery along certain 4-valent plumbing graphs. This way all the graph classes from [5] have a representative which admits a rational blowdown leading to an exotic manifold. We emphasize the simplicity of the constructions which boils down to finding a good configuration of complex lines and quadrics in CP 2 , and deciding which intersections to blow up. [ABSTRACT FROM AUTHOR]

Suh (Math. Nachr. 290 (2017) 442–451) proved that there are no Hopf real hypersurfaces in the complex quadric that have parallel normal Jacobi operators. Motivated by this result, in this paper, we introduce the notions of C‐parallel and Reeb parallel for normal Jacobi operators, which generalize the notion 'parallel'. First we obtain a non‐existence theorem of Hopf real hypersurfaces with C‐parallel normal Jacobi operator in the complex quadric Qm for m⩾3. We then prove that a Hopf real hypersurface has a Reeb parallel normal Jacobi operator if and only if it has an A‐isotropic singular normal vector field. [ABSTRACT FROM AUTHOR]

Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics from the point of view of Mori theory. We compute their effective, nef and movable cones, the generators of their Cox rings, and their groups of pseudo-automorphisms. Furthermore, we give a complete description of both the Mori chamber and stable base locus decompositions of the effective cone of the space of complete collineations of the three-dimensional projective space. [ABSTRACT FROM AUTHOR]