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On the X-rank with respect to linear projections of projective varieties
- Source :
- Ballico, Edoardo ; Bernardi, Alessandra (2009) On the X-rank with respect to linear projections of projective varieties. [Preprint], Mathematical News / Mathematische Nachrichten, Mathematical News / Mathematische Nachrichten, 2011, 284 (17-18), pp.2133-2140. ⟨10.1002/mana.200910275⟩, Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2011, 284 (17-18), pp.2133-2140. ⟨10.1002/mana.200910275⟩
- Publication Year :
- 2009
-
Abstract
- In this paper we improve the known bound for the $X$-rank $R_{X}(P)$ of an element $P\in {\mathbb{P}}^N$ in the case in which $X\subset {\mathbb P}^n$ is a projective variety obtained as a linear projection from a general $v$-dimensional subspace $V\subset {\mathbb P}^{n+v}$. Then, if $X\subset {\mathbb P}^n$ is a curve obtained from a projection of a rational normal curve $C\subset {\mathbb P}^{n+1}$ from a point $O\subset {\mathbb P}^{n+1}$, we are able to describe the precise value of the $X$-rank for those points $P\in {\mathbb P}^n$ such that $R_{X}(P)\leq R_{C}(O)-1$ and to improve the general result. Moreover we give a stratification, via the $X$-rank, of the osculating spaces to projective cuspidal projective curves $X$. Finally we give a description and a new bound of the $X$-rank of subspaces both in the general case and with respect to integral non-degenerate projective curves.<br />10 pages
- Subjects :
- Linearly normal curve
MAT/03 Geometria
General Mathematics
[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]
010103 numerical & computational mathematics
Rank (differential topology)
Rational normal curve
Commutative Algebra (math.AC)
01 natural sciences
Projection (linear algebra)
Combinatorics
Mathematics - Algebraic Geometry
FOS: Mathematics
0101 mathematics
Algebraic Geometry (math.AG)
Projective variety
Mathematics
Rank
Secant Varieties
Rational Normal Curves
Projections
010102 general mathematics
Mathematics - Commutative Algebra
Linear subspace
SYMMETRIC TENSORS
rank
14N05, 14H50
Tangential varietie
SECANT VARIETIES
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Element (category theory)
Subspace topology
Osculating circle
Subjects
Details
- Language :
- Italian
- ISSN :
- 0025584X and 15222616
- Database :
- OpenAIRE
- Journal :
- Ballico, Edoardo ; Bernardi, Alessandra (2009) On the X-rank with respect to linear projections of projective varieties. [Preprint], Mathematical News / Mathematische Nachrichten, Mathematical News / Mathematische Nachrichten, 2011, 284 (17-18), pp.2133-2140. ⟨10.1002/mana.200910275⟩, Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2011, 284 (17-18), pp.2133-2140. ⟨10.1002/mana.200910275⟩
- Accession number :
- edsair.doi.dedup.....7ea5a0e76da986007a85418c7b837813