Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau
  manifolds   We investigate a potential relationship between mirror symmetry for
Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and
Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a
so-called Tyurin degeneration to a union of two Fano varieties, then one should
be able to construct a mirror to that Calabi-Yau by gluing together the
Landau-Ginzburg models of those two Fano varieties. We provide evidence for
this correspondence in a number of different settings, including
Batyrev-Borisov mirror symmetry for K3 surfaces and Calabi-Yau threefolds,
Dolgachev-Nikulin mirror symmetry for K3 surfaces, and an explicit family of
threefolds that are not realized as complete intersections in toric varieties.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph