Generalizations of Strassen's equations for secant varieties of Segre varieties

TL;DR

This paper introduces new modules of equations for secant varieties of Segre varieties, extending Strassen's equations by constructing matrix subspaces from tensors with specific commutation properties.

Contribution

It generalizes Strassen's equations by defining new modules of equations derived from tensors with particular commutation properties for secant varieties.

Findings

New modules of equations for secant varieties of Segre varieties

Generalization of Strassen's commutation equations

Construction of matrix subspaces satisfying commutation properties

Abstract

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations. Our modules of equations are obtained by constructing subspaces of matrices from tensors that satisfy various commutation properties.