Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric semi-perfect obstruction theory revisited   In this paper we survey some results on the symmetric semi-perfect
obstruction theory on a Deligne-Mumford stack $X$ constructed by Chang-Li, and
Behrend's theorem equating the weighted Euler characteristic of $X$ and the
virtual count of $X$ by symmetric semi-perfect obstruction theories. As an
application, we prove that Joyce's d-critical scheme admits a symmetric
semi-perfect obstruction theory, which can be applied to the virtual Euler
characteristics by Jiang-Thomas.

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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph