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
2016-06-27
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,