### Abstract

Let X be the toric variety (P1)4 associated with its four-dimensional polytope Δ. Denote by X the resolution of the singular Fano variety X° associated with the dual polytope A°. Generically, anticanonical sections Y of X and anticanonical sections Y of X are mirror partners in the sense of Batyrev. Our main result is the following: The Hodge- Theoretic mirror of the quotient Z associated to a maximal admissible pair (Y, G) in X is not a quotient Z associated to an admissible pair in X. Nevertheless, it is possible to construct a mirror orbifold for Z by means of a quotient of a suitable Y. Its crepant resolution is a Calabi-Yau threefold with Hodge numbers (8,4). Instead, if we start from a non-maximal admissible pair, in the same case, its mirror is the quotient associated to an admissible pair.

Lingua originale | English |
---|---|

pagine (da-a) | 709-729 |

Numero di pagine | 21 |

Rivista | ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE |

Volume | 15 |

Stato di pubblicazione | Published - 2016 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Mathematics (miscellaneous)

## Fingerprint Entra nei temi di ricerca di 'A closer look at mirrors and quotients of Calabi-Yau threefolds'. Insieme formano una fingerprint unica.

## Cita questo

Bini, G., Favale, F. F., & Bini, G. (2016). A closer look at mirrors and quotients of Calabi-Yau threefolds.

*ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE*,*15*, 709-729.