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# 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 (1965 - 2019), 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 $X$.
Document type :
Journal articles
Domain :

https://hal.inria.fr/hal-00646161
Contributor : Alessandra Bernardi Connect in order to contact the contributor
Submitted on : Tuesday, November 29, 2011 - 1:04:10 PM
Last modification on : Thursday, August 4, 2022 - 4:52:38 PM

### Citation

Edoardo Ballico, Alessandra Bernardi. On the X-rank with respect to linearly normal curves. Collectanea Mathematica, 2011, 64 (2), pp.141-154. ⟨10.1007/s13348-011-0058-4⟩. ⟨hal-00646161⟩

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