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.
|Numero di pagine||12|
|Rivista||Journal of Algebraic Geometry|
|Stato di pubblicazione||Published - 2012|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology