Examples of Calabi-Yau threefolds parametrised by Shimura varieties

Details Examples of Calabi-Yau threefolds parametrised by Shimura varieties Examples of Calabi-Yau threefolds parametrised by Shimura varieties

2010-05-04

arxiv.org/abs/1005.0478v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

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.

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