On the X-rank with respect to linearly normal curves

Edoardo Ballico; Alessandra Bernardi

doi:10.1007//s13348-011-0058-4

paper

On the X-rank with respect to linearly normal curves

arXiv:1002.1578 · doi:10.1007//s13348-011-0058-4

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 $X$ .