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EnglishIn a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard-Fuchs equation associated to the holomorphic -form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this result. Using a construction due to Shioda, we also relate certain quotients of these one-parameter families to the family of Mirror Quintics. Our constructions generalize to degree n Calabi-Yau varieties in (n - 1)-dimensional projective space.
G. Bini, B. van Geemen, & T.L. Kelly (2012). Mirror quintics, discrete symmetries and Shioda maps. JOURNAL OF ALGEBRAIC GEOMETRY, 21(3), 401-412.
| Data di pubblicazione: | 2012 |
| Titolo: | Mirror quintics, discrete symmetries and Shioda maps |
| Autori: | |
| Citazione: | G. Bini, B. van Geemen, & T.L. Kelly (2012). Mirror quintics, discrete symmetries and Shioda maps. JOURNAL OF ALGEBRAIC GEOMETRY, 21(3), 401-412. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1090/S1056-3911-2011-00544-4 |
| Abstract: | In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard-Fuchs equation associated to the holomorphic -form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this result. Using a construction due to Shioda, we also relate certain quotients of these one-parameter families to the family of Mirror Quintics. Our constructions generalize to degree n Calabi-Yau varieties in (n - 1)-dimensional projective space. |
| Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/10447/394796
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