Padded polynomials, their cousins, and geometric complexity theory

Details Padded polynomials, their cousins, and geometric complexity theory Padded polynomials, their cousins, and geometric complexity theory

2012-04-20

arxiv.org/abs/1204.4693v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

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.

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