2008/09/10 by Bini, Gilberto, van Geemen, Bert, Kelly, Tyler L.
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.0809.1791
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.