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
Mirror quintics, discrete symmetries and Shioda maps / G. Bini, B. van Geemen, T.L. Kelly. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 21:3(2012), pp. PII S1056-3911(2011)00544-4.401-PII S1056-3911(2011)00544-4.412.
Mirror quintics, discrete symmetries and Shioda maps
G. BiniPrimo
;B. van GeemenSecondo
;
2012
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 MirrorFile | Dimensione | Formato | |
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