The $b$-secant variety of a smooth curve has a codimension $1$ locally closed subset whose points have rank at least $b+1$

Abstract

Take a smooth, connected and non-degenerate projective curve $X\subset {\mathbb{P}}^r$, $r\ge 2b+2\ge 6$, defined over an algebraically closed field with characteristic $0$ and let ${\sigma }_b(X)$ be the $b$-secant variety of $X$. We prove that the $X$-rank of $q$ is at least $b+1$ for a non-empty codimension $1$ locally closed subset of ${\sigma }_b(X)$.

References in corpus (1)

• Computing symmetric rank for symmetric tensors