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 settheoretic equations, a description of the ideal in terms of the kernel of a linear map that generalizes the FoulkesHowe map, and an explicit description of the coordinate ring of the normalization. We also prove asymptotic injectivity of the FoulkesHowe map.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1204.4693
 Bibcode:
 2012arXiv1204.4693K
 Keywords:

 Mathematics  Algebraic Geometry;
 Computer Science  Computational Complexity;
 Mathematics  Representation Theory;
 14MXX;
 68Q15;
 14L30
 EPrint:
 8 pages