On the stratification by $X$-ranks of a linearly normal elliptic curve $X\subset {\mathbb{P}}^n$

Abstract

Let $X\subset {\mathbb{P}}^n$ be a linearly normal elliptic curve. For any $P\in {\mathbb{P}}^n$ the $X$-rank of $P$ is the minimal cardinality of a set $S\subset X$ such that $P\in ⟨S⟩$. In this paper we give an almost complete description of the stratification of ${\mathbb{P}}^n$ given by the $X$-rank and the open $X$-rank.

Added a result on the open rank

References in corpus (2)

• Computing symmetric rank for symmetric tensors
• Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture