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

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posted on 17.09.2018, 12:22 by Charles F. Doran, Andrew Harder, Alan Thompson
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of Symposia in Pure Mathematics

Volume

96

Pages

93 - 131

Citation

DORAN, C.F., HARDER, A. and THOMPSON, A., 2017. Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds. Proceedings of Symposia in Pure Mathematics, 96, pp. 93-131

Publisher

American Mathematical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

27/06/2016

Publication date

2017-11-24

Notes

First published in Proceedings of Symposia in Pure Mathematics, in 96, pp. 93-131, 2017, published by the American Mathematical Society,

ISSN

0082-0717

Language

en

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