Generalizations of Strassen's Equations for Secant Varieties of Segre Varieties

Abstract

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations (Strassen, 1988). Our modules of equations are obtained by constructing subspaces of matrices from tensors that satisfy various commutation properties.

Key Words:

• Border
• Secant varieties
• Segre varieties
• Strassen's equations

2000 Mathematics Subject Classification:

• Primary 15A69, 14N05
• Secondary 03D15

ACKNOWLEDGMENT

Landsberg is supported by NSF grant DMS-0305829.

Notes

Communicated by L. Ein.