Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable spherical varieties and their moduli   We introduce a notion of stable spherical variety which includes the
spherical varieties under a reductive group $G$ and their flat equivariant
degenerations. Given any projective space $\bP$ where $G$ acts linearly, we
construct a moduli space for stable spherical varieties over $\bP$, that is,
pairs $(X,f)$, where $X$ is a stable spherical variety and $f : X \to \bP$ is a
finite equivariant morphism. This space is projective, and its irreducible
components are rational. It generalizes the moduli space of pairs $(X,D)$,
where $X$ is a stable toric variety and $D$ is an effective ample Cartier
divisor on $X$ which contains no orbit. The equivariant automorphism group of
$\bP$ acts on our moduli space; the spherical varieties over $\bP$ and their
stable limits form only finitely many orbits. A variant of this moduli space
gives another view to the compactifications of quotients of thin Schubert cells
constructed by Kapranov and Lafforgue.

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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
19
The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci