Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix orbit closures   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.

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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga