Padded Polynomials, Their Cousins, and Geometric Complexity Theory

Abstract

We establish basic facts about the varieties of homogeneous polynomials divisible by powers of linear forms, and explain consequences for geometric complexity theory. This includes quadratic set-theoretic equations, a description of the ideal in terms of the kernel of a linear map that generalizes the Foulkes–Howe map, and an explicit description of the coordinate ring of the normalization. We also prove asymptotic injectivity of the Foulkes–Howe map.

Key Words:

• Chow variety
• Foulkes–Howe conjecture
• Geometric complexity theory
• Padded polynomials

2000 Mathematics Subject Classification:

• 68Q17
• 14N05

ACKNOWLEDGMENTS

We thank Michel Brion, Jaydeep Chipalkatti, and Jerzy Weyman for useful conversations.

Kadish is supported by DOE ASCR grant DE-SC0002505 (Topology for Statistical Modeling of Petascale Data). Landsberg is supported by NSF grant DMS-1006353.

Notes

Communicated by R. Piene.