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EnglishLet X be the toric variety (P^1)^4 associated with its four-dimensional polytope. Consider a resolution of the singular Fano variety associated with the dual polytope of X. Generically, anti-canonical sections Y of X and anticanonical sections of the resolution 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 associated to an admissible pair in the resolution. Nevertheless, it is possible to construct a mirror orbifold of Z by means of a quotient of a suitable anticanonical section of the resolution. The crepant resolution of Z is a Calabi-Yau threeefold with Hodge numbers (8, 4). Instead, if we start from a non-maximal admissible pair, in same cases, its mirror is the quotient associated to an admissible pair.
| Data di pubblicazione: | 2016 |
| Titolo: | A closer look at quotients and their mirrors |
| Autori: | |
| Citazione: | G. Bini, & F.F. Favale (2016). A closer look at quotients and their mirrors. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, XV special issue, 709-729. |
| Rivista: | |
| Digital Object Identifier (DOI): | 10.2422/2036-2145.201312_003 |
| Abstract: | Let X be the toric variety (P^1)^4 associated with its four-dimensional polytope. Consider a resolution of the singular Fano variety associated with the dual polytope of X. Generically, anti-canonical sections Y of X and anticanonical sections of the resolution 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 associated to an admissible pair in the resolution. Nevertheless, it is possible to construct a mirror orbifold of Z by means of a quotient of a suitable anticanonical section of the resolution. The crepant resolution of Z is a Calabi-Yau threeefold with Hodge numbers (8, 4). Instead, if we start from a non-maximal admissible pair, in same cases, its mirror is the quotient associated to an admissible pair. |
| URL: | http://annaliscienze.sns.it/index.php?page=Article&id=406 |
| Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/10447/399914
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