Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable varieties with a twist   We describe a new approach to the definition of the moduli functor of stable
varieties. While there is wide agreement as to what classes of varieties should
appear, the notion of a family of stable surfaces is quite subtle, as key
numerical invariants may fail to be constant in flat families. Our approach is
to add natural stack structure to stable varieties. For example, given a
canonical model we take the global-quotient stack structure arising from its
realization as Proj of the canonical ring. Deformations of the stack structure
preserve key numerical invariants of the stable variety, including the top
self-intersection of the canonical divisor. This approach yields a transparent
construction of the moduli stack of stable varieties as a global quotient of a
suitable Hilbert scheme of weighted projective stacks.

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The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg