Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mirror symmetry for log Calabi-Yau surfaces I   We give a canonical synthetic construction of the mirror family to a pair
(Y,D) of a smooth projective surface with an anti-canonical cycle of rational
curves, as the spectrum of an explicit algebra defined in terms of counts of
rational curves on Y meeting D in a single point. In the case D is
contractible, the family gives a smoothing of the dual cusp, and thus a proof
of Looijenga's 1981 cusp conjecture.

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The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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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: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ