# On the X-rank with respect to linearly normal curves

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 study the $X$-rank of points with respect to smooth linearly normal curves $X\subset \PP n$ of genus $g$ and degree $n+g$. We prove that, for such a curve $X$, under certain circumstances, the $X$-rank of a general point of $X$-border rank equal to $s$ is less or equal than $n+1-s$. In the particular case of $g=2$ we give a complete description of the $X$-rank if $n=3,4$; while if $n\geq 5$ we study the $X$-rank of points belonging to the tangential variety of $X$.
Type de document :
Article dans une revue
Collectanea Mathematica, Universitat de Barcellona, 2011
Domaine :

https://hal.inria.fr/hal-00646161
Contributeur : Alessandra Bernardi <>
Soumis le : mardi 29 novembre 2011 - 13:04:10
Dernière modification le : jeudi 11 janvier 2018 - 16:14:55

### Identifiants

• HAL Id : hal-00646161, version 1
• ARXIV : 1002.1578

### Citation

Edoardo Ballico, Alessandra Bernardi. On the X-rank with respect to linearly normal curves. Collectanea Mathematica, Universitat de Barcellona, 2011. 〈hal-00646161〉

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