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EnglishLet 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.
G. Bini, & F.F. Favale (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.
| Data di pubblicazione: | 2016 | |
| Titolo: | A closer look at mirrors and quotients of Calabi-Yau threefolds | |
| Autori: | ||
| Citazione: | G. Bini, & F.F. Favale (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. | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.2422/2036-2145.201312_003 | |
| 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. | |
| 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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