Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homological mirror symmetry for hypersurface cusp singularities   We study versions of homological mirror symmetry for hypersurface cusp
singularities and the three hypersurface simple elliptic singularities. We show
that the Milnor fibres of each of these carries a distinguished Lefschetz
fibration; its derived directed Fukaya category is equivalent to the derived
category of coherent sheaves on a smooth rational surface $Y_{p,q,r}$. By using
localization techniques on both sides, we get an isomorphism between the
derived wrapped Fukaya category of the Milnor fibre and the derived category of
coherent sheaves on a quasi-projective surface given by deleting an
anti-canonical divisor $D$ from $Y_{p,q,r}$. In the cusp case, the pair
$(Y_{p,q,r}, D)$ is naturally associated to the dual cusp singularity, tying
into Gross, Hacking and Keel's proof of Looijenga's conjecture.

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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph