Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic Gromov-Witten invariants   The goal of this paper is to give a general theory of logarithmic
Gromov-Witten invariants. This gives a vast generalization of the theory of
relative Gromov-Witten invariants introduced by Li-Ruan, Ionel-Parker, and Jun
Li, and completes a program first proposed by the second named author in 2002.
One considers target spaces X carrying a log structure. Domains of stable log
curves are log smooth curves. Algebraicity of the stack of such stable log maps
is proven, subject only to the hypothesis that the log structure on X is fine,
saturated, and Zariski. A notion of basic stable log map is introduced; all
stable log maps are pull-backs of basic stable log maps via base-change. With
certain additional hypotheses, the stack of basic stable log maps is proven to
be proper. Under these hypotheses and the additional hypothesis that X is log
smooth, one obtains a theory of log Gromov-Witten invariants.

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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int