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

Charles F. Doran, Andrew Harder, Alan Thompson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationproceedings of the conference String-Math, 2015
EditorsWei Song, Bong H. Lian, Si Li, Shing-Tung Yau
PublisherAmerican Mathematical Society
Pages93-131
Number of pages39
Volume96
ISBN (Electronic)9781470442767
ISBN (Print)9781470429515
DOIs
StatePublished - Jan 1 2017
Externally publishedYes
Eventproceedings of the conference String-Math, 2015 - Sanya, China
Duration: Dec 31 2015Jan 4 2016

Other

Otherproceedings of the conference String-Math, 2015
CountryChina
CitySanya
Period12/31/151/4/16

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Keywords

  • Calabi-Yau threefold
  • Degeneration
  • Fibration
  • K3 surface
  • Mirror symmetry

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Doran, C. F., Harder, A., & Thompson, A. (2017). Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds. In W. Song, B. H. Lian, S. Li, & S-T. Yau (Eds.), proceedings of the conference String-Math, 2015 (Vol. 96, pp. 93-131). American Mathematical Society. https://doi.org/10.1090/pspum/096/01655