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Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds

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arxiv 1601.08110 v3 pith:EGZJ7Q45 submitted 2016-01-29 math.AG

Charles F. Doran , Andrew Harder , Alan Thompson This is my paper · ORCID
classification math.AG
keywords mirrorcalabi-yausymmetryvarietiesfanolandau-ginzburgmanifoldsmodels
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fano and Reflexive Polytopes from Feynman Integrals

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.

  2. Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces

    hep-th 2024-03 unverdicted novelty 5.0 of 10

    Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.

  3. Advancements in Functorial Homological Mirror Symmetry

    hep-th 2025-02 reject novelty 4.0 of 10

    A programmatic review asserting that stability and transversality in Donaldson-Thomas degeneracy formulas correspond to abelian versus nonabelian gauging in Rozansky-Witten theory, without providing a derivation.

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