Examples of Calabi-Yau threefolds parametrised by Shimura varieties

Abstract

These are notes from talks of the authors on some explicit examples of families of Calabi-Yau threefolds which are parametrised by a Shimura variety. We briefly review the periods of Calabi-Yau threefolds and we discuss a recent result on Picard-Fuchs equations for threefolds which are hypersurfaces with many automorphisms. Next various examples of families parametrised by Shimura varieties are given. Most of these are due to J.C. Rohde. The examples with an automorphism of order three are given in some detail. We recall that such families do not have maximally unipotent monodromy and that the Shimura varieties in these cases are ball quotients.

15 pages

References in corpus (5)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
• Disproof of modularity of moduli space of CY 3-folds of double covers of P3 ramified along eight planes in general positions
• Quotients of Hypersurfaces in Weighted Projective Space
• Mirror Quintics, discrete symmetries and Shioda Maps