@inproceedings{265c611287fc46ffbbe511b9fb275077,

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

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.",

keywords = "Calabi-Yau threefold, Degeneration, Fibration, K3 surface, Mirror symmetry",

author = "Doran, {Charles F.} and Andrew Harder and Alan Thompson",

year = "2017",

doi = "10.1090/pspum/096/01655",

language = "English (US)",

isbn = "9781470429515",

series = "Proceedings of Symposia in Pure Mathematics",

publisher = "American Mathematical Society",

pages = "93--131",

editor = "Wei Song and Lian, {Bong H.} and Si Li and Shing-Tung Yau",

booktitle = "proceedings of the conference String-Math, 2015",

address = "United States",

note = "proceedings of the conference String-Math, 2015 ; Conference date: 31-12-2015 Through 04-01-2016",

}