# On the X-rank with respect to linear projections of projective varieties

2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
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.
Type de document :
Article dans une revue
Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2011, 284 (17-18), pp.2133-2140. 〈10.1002/mana.200910275〉
Domaine :

https://hal.inria.fr/hal-00646117
Contributeur : Alessandra Bernardi <>
Soumis le : mardi 29 novembre 2011 - 11:34:06
Dernière modification le : vendredi 12 janvier 2018 - 01:48:43

### Citation

Edoardo Ballico, Alessandra Bernardi. On the X-rank with respect to linear projections of projective varieties. Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2011, 284 (17-18), pp.2133-2140. 〈10.1002/mana.200910275〉. 〈hal-00646117〉

### Métriques

Consultations de la notice