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arXiv · 1002.1578

On the X-rank with respect to linearly normal curves

Edoardo Ballico·Alessandra Bernardi
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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 $X$.

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Edoardo Ballico, Alessandra Bernardi. 2010-02-08. On the X-rank with respect to linearly normal curves. https://doi.org/10.1007//s13348-011-0058-4

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