Vector bundles give equations of cactus varieties

TL;DR

This paper demonstrates how vector bundles can be used to derive equations for cactus varieties, but these equations are insufficient to define secant varieties of Veronese varieties in general.

Contribution

It establishes a connection between vector bundles and equations of cactus varieties, highlighting limitations for secant varieties of Veronese varieties.

Findings

Vector bundles provide equations for cactus varieties.

Equations from vector bundles are insufficient for secant varieties.

Highlights limitations of vector bundle methods for certain varieties.

Abstract

We prove that vector bundles give equations of cactus varieties. We derive from it that equations coming from vector bundles are not enough to define secant varieties of Veronese varieties in general.