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We prove that for every smooth prime Fano $3$-fold $V$, the Hilbert scheme $\operatorname{Hilb}^{sc} V$ of smooth connected curves on $V$ contains a generically non-reduced irreducible component of Mumford type. We also study the deformations of degenerate curves $C$ in $V$, i.e., curves $C$ contained in a smooth anti-canonical member $S \in |-K_V|$ of $V$. We give a sufficient condition for $C$ to be stably degenerate, i.e., every small (and global) deformation of $C$ in $V$ is contained in a deformation of $S$ in $V$. As a result, by using the Hilbert-flag scheme of $V$, we determine the dimension and the smoothness of $\operatorname{Hilb}^{sc} V$ at the point $[C]$, assuming that the class of $C$ in $\operatorname{Pic} S$ is generated by $-K_V\big{\vert}_S$ together with the class of a line, or a conic on $V$., 20 pages, final version, to appear in Mathematische Nachrichten

We have established an apparatus for terahertz and mid-infrared spectroscopy in an ultrahigh vacuum and have measured absorption spectra of D

We measured infrared absorption spectra of crystalline II of CH4 and succeeded in detecting a prominent Q(2) peak in the ν3 vibrational region by rapid cooling after annealing as well as previously reported rovibrational and librational-vibrational peaks. The integral intensities of the R(0), R(1), and Q(2) peaks were found to show biexponential dependence on time. This clearly demonstrates the interconversion among the three nuclear-spin isomers occupying low-lying rotational levels. The two relaxation rates obtained by biexponential fitting were (0.48, 2.3), (1.1, 4.1), (2.3, 5.1), and (3.4, 15.3) in units of inverse hour (h−1) at 5.2, 6.0, 6.5, and 7.0 K, respectively.

We study the deformations of a curve $C$ on an Enriques-Fano $3$-fold $X \subset \mathbb P^n$, assuming that $C$ is contained in a smooth hyperplane section $S \subset X$, that is a smooth Enriques surface in $X$. We give a sufficient condition for $C$ to be (un)obstructed in $X$, in terms of half pencils and $(-2)$-curves on $S$. Let $\operatorname{Hilb}^{sc} X$ denote the Hilbert scheme of smooth connected curves in $X$. By using the Hilbert-flag scheme of $X$, we also compute the dimension of $\operatorname{Hilb}^{sc} X$ at $[C]$ and give a sufficient condition for $\operatorname{Hilb}^{sc} X$ to contain a generically non-reduced irreducible component of Mumford type., Comment: 18 pages, final version, to appear in Journal of Pure and Applied Algebra

In this paper, we study the deformations of curves in the projective 3-space $\mathbb P^3$ (space curves), one of the most classically studied objects in algebraic geometry. We prove a conjecture due to J. O. Kleppe (in fact, a version modified by Ph. Ellia) concerning maximal families of space curves lying on a smooth cubic surface, assuming the quadratic normality of its general members. We also give a sufficient condition for curves lying on a cubic surface to be obstructed in $\mathbb P^3$ in terms of lines on the surface. For the proofs, we use the Hilbert-flag scheme of $\mathbb P^3$ as a main tool and apply a recent result on primary obstructions to deforming curves on a threefold developed by S. Mukai and the author., Comment: 24 pages, final version, to appear in Manuscripta Mathematica

In this paper, we make a correction to Theorem 3.3 of the aforementioned paper (Internat. J. Math. 28(13) (2017) 1750099). We also provide a counterexample to the theorem and point out an error in the proof.

We have established an apparatus for terahertz and mid-infrared spectroscopy in an ultrahigh vacuum and have measured absorption spectra of D2O clusters trapped in solid Ar. To assign terahertz absorption peaks due to the D2O dimer, trimer, and tetramer, the dependence of the spectrum on the annealing temperature and D2O dilution was analyzed. The assignment was also examined by ab initio calculations with the use of the “our own N-layered integrated molecular orbital and molecular mechanics” method, where the flexibility of surrounding Ar atoms was systematically incorporated. We identified all the intermolecular fundamentals of the dimer and those with significant intensities of the trimer and tetramer, whose structural symmetries were revealed to be broken down. After isolating the D2O clusters in solid Ar, we sublimated only Ar atoms to leave behind matrix-sublimation ice, which was found to be amorphous- or crystal-like depending on the formation conditions: the dilution and sublimation temperature. The crystallinity of matrix-sublimation ice was determined by decomposing its terahertz spectrum into the spectra of amorphous and crystalline ices. Since the crystallinity got higher by raising the dilution and sublimation temperature, the diffusion of the D2O monomer on the surface of sublimating solid Ar was found to be crucial to the crystallization of the sublimation ice.

We study the Hilbert scheme (Hilb V) of smooth connected curves on a smooth del Pezzo 3-fold V. We prove that every degenerate curve C, i.e. every curve contained in a smooth hyperplane section S of V, does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) the Euler characteristic of the twisted ideal sheaf I_C(S) of C is greater than or equal to one, and (ii) for every line E on S which is disjoint to C, the normal bundle of E in V is trivial. As a consequence, we prove an analogue (for Hilb V) of a conjecture of J.O.Kleppe which is concerned with non-reduced components of the Hilbert scheme (Hilb P^3) of curves in the 3-dimensional projective space P^3., v2: 26 pages; Section 4 rewritten; proof of Prop. 4.12 improved; proof of Lem. 4.10 corrected; references added

Let denote the Hilbert scheme of smooth connected curves of degree d and genus g in the projective 3-space ℙ3. We describe all irreducible components V of for every integer d ≤ 16. For each component V, we compute the dimension of V and determine whether is generically smooth along V or not. We show that if d ≥ 91, then has a unique irreducible component whose general member is contained in a smooth cubic surface, along which is generically smooth.

We give a sufficient condition for a first order infinitesimal deformation of a curve on a 3 3 -fold to be obstructed. As application we construct generically non-reduced components of the Hilbert schemes of uniruled 3 3 -folds and the Hom scheme from a general curve of genus five to a general cubic 3 3 -fold.

Let $Hilb P^3$ denote the Hilbert scheme of smooth connected curves in $P^3$. We consider maximal irreducible closed subsets $W \subset Hilb P^3$ whose general member $C$ is contained in a smooth cubic surface and investigate the conditions for $W$ to be a component of $(Hilb P^3)_{red}$. We especially study the case where the dimension of the tangent space of $Hilb P^3$ at $[C]$ is greater than $\dim W$ by one. We compute obstructions to deforming $C$ in $P^3$ and prove that for every $W$ in this case, $Hilb P^3$ is non-reduced along $W$ and $W$ is a component of $(Hilb P^3)_{red}$., 22 pages, 1 figure, to appear in Publ. RIMS, Kyoto University