Secant varieties of P^2 x P^n embedded by O(1,2)

TL;DR

This paper explicitly describes the defining equations and Schur module decompositions for secant varieties of P^2 x P^n embedded by O(1,2), extending previous matrix construction methods.

Contribution

It provides new explicit matrix equations and Schur module decompositions for secant varieties of P^2 x P^n, generalizing prior approaches.

Findings

Explicit equations for secant varieties up to r=5.

Schur module decompositions of generators.

Extension of matrix construction methods.

Abstract

We describe the defining ideal of the rth secant variety of P^2 x P^n embedded by O(1,2), for arbitrary n and r at most 5. We also present the Schur module decomposition of the space of generators of each such ideal. Our main results are based on a more general construction for producing explicit matrix equations that vanish on secant varieties of products of projective spaces. This extends previous work of Strassen and Ottaviani.