Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mirror Symmetry in dimension one and Fourier-Mukai equivalences   In this paper we will describe an approach to mirror symmetry for appropriate
1-dimensional DM stacks of arithmetic genus $g \leq 1$, called tcnc curves,
which was developed by the author with Treumann and Zaslow in arXiv:1103.2462 .
This involves introducing a conjectural sheaf-theoretic model for the Fukaya
category of punctured Riemann surfaces. As an application, we will investigate
derived equivalences of tcnc curves, and generalize classic results of Mukai on
dual abelian varieties (Mukai 1981).

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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-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: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex