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

Charles F. Doran; Andrew Harder; Alan Thompson

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arXiv · 1601.08110

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

Charles F. Doran·Andrew Harder·Alan Thompson

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Abstract

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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Charles F. Doran, Andrew Harder, Alan Thompson. 2016-01-29. Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds. https://arxiv.org/abs/1601.08110

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