Mirror Quintics, discrete symmetries and Shioda Maps

Details Mirror Quintics, discrete symmetries and Shioda Maps Mirror Quintics, discrete symmetries and Shioda Maps

2008-09-10

arxiv.org/abs/0809.1791v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

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 3-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.

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