### 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) |
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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 | |

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 |
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Country | China |

City | Sanya |

Period | 12/31/15 → 1/4/16 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*proceedings of the conference String-Math, 2015*(Vol. 96, pp. 93-131). American Mathematical Society. https://doi.org/10.1090/pspum/096/01655