Matrix orbit closures

Andrew Berget; Alex Fink

Matrix orbit closures

Algebraic Geometry 2015-07-20 v6 Commutative Algebra Combinatorics

Authors: Andrew Berget , Alex Fink

Abstract

Let $G$ be the group $GL_r(C) \times (C^\times)^n$ . We conjecture that the finely-graded Hilbert series of a $G$ orbit closure in the space of $r$ -by- $n$ matrices is wholly determined by the associated matroid. In support of this, we prove that the coefficients of this Hilbert series corresponding to certain hook-shaped Schur functions in the $GL_r(C)$ variables are determined by the matroid, and that the orbit closure has a set-theoretic system of ideal generators whose combinatorics are also so determined. We also discuss relations between these Hilbert series for related matrices, including their stabilizing behaviour as $r$ increases.

Keywords

nilpotent orbits matroid theory periodic orbits in hamiltonian systems

Cite

@article{arxiv.1306.1810,
  title  = {Matrix orbit closures},
  author = {Andrew Berget and Alex Fink},
  journal= {arXiv preprint arXiv:1306.1810},
  year   = {2015}
}

Comments

The proof of the main theorem (Theorem 5.1) of v5, asserting the invariance of the equivariant K-class of a matrix orbit closure, was incorrect and has been removed

Matrix orbit closures

Abstract

Keywords

Cite

Comments

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