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.

G. Bini, B. van Geemen, T.L. Kelly (2012). Mirror quintics, discrete symmetries and Shioda maps. JOURNAL OF ALGEBRAIC GEOMETRY, 21(3), 401-412 [10.1090/S1056-3911-2011-00544-4].

Mirror quintics, discrete symmetries and Shioda maps

G. Bini;B. van Geemen;
2012-01-01

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 MAT/03 - Geometria
G. Bini, B. van Geemen, T.L. Kelly (2012). Mirror quintics, discrete symmetries and Shioda maps. JOURNAL OF ALGEBRAIC GEOMETRY, 21(3), 401-412 [10.1090/S1056-3911-2011-00544-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/394796
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