Tangential varieties of Segre-Veronese varieties

TL;DR

This paper characterizes the defining equations and representation-theoretic structure of the tangential variety of Segre-Veronese varieties, confirming a conjecture in the special case of Segre varieties.

Contribution

It provides the minimal generators of the ideal of the tangential variety and describes its coordinate ring's decomposition, advancing understanding of these algebraic varieties.

Findings

Determined minimal generators of the tangential variety's ideal.

Decomposed the coordinate ring into irreducible GL-representations.

Confirmed Landsberg and Weyman's conjecture for Segre varieties.

Abstract

We determine the minimal generators of the ideal of the tangential variety of a Segre-Veronese variety, as well as the decomposition into irreducible GL-representations of its homogeneous coordinate ring. In the special case of a Segre variety, our results confirm a conjecture of Landsberg and Weyman.