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

Charles F. Doran; Andrew Harder; Alan Thompson

doi:10.1090/pspum/096/01655

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

Charles F. Doran, Andrew Harder, Alan Thompson

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	proceedings of the conference String-Math, 2015
Editors	Wei Song, Bong H. Lian, Si Li, Shing-Tung Yau
Publisher	American Mathematical Society
Pages	93-131
Number of pages	39
Volume	96
ISBN (Electronic)	9781470442767
ISBN (Print)	9781470429515
DOIs	https://doi.org/10.1090/pspum/096/01655
State	Published - Jan 1 2017
Externally published	Yes
Event	proceedings of the conference String-Math, 2015 - Sanya, China Duration: Dec 31 2015 → Jan 4 2016

Other

Other	proceedings of the conference String-Math, 2015
Country	China
City	Sanya
Period	12/31/15 → 1/4/16

Fingerprint

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

Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds. / Doran, Charles F.; Harder, Andrew; Thompson, Alan.

proceedings of the conference String-Math, 2015. ed. / Wei Song; Bong H. Lian; Si Li; Shing-Tung Yau. Vol. 96 American Mathematical Society, 2017. p. 93-131.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Doran, CF, Harder, A & Thompson, A 2017, Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds. in W Song, BH Lian, S Li & S-T Yau (eds), proceedings of the conference String-Math, 2015. vol. 96, American Mathematical Society, pp. 93-131, proceedings of the conference String-Math, 2015, Sanya, China, 12/31/15. https://doi.org/10.1090/pspum/096/01655

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Access to Document

10.1090/pspum/096/01655