Padded Polynomials, Their Cousins, and Geometric Complexity Theory
Harlan Kadish, Joseph M. Landsberg · Communications in Algebra · 2014
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.