Mirror quintics, discrete symmetries and Shioda maps

Gilberto Bini, Tyler L. Kelly, Bert Van Geemen, Gilberto Bini

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)401-412
Number of pages12
JournalJournal of Algebraic Geometry
Publication statusPublished - 2012

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


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