Starting from extremal elliptic surfaces, we construct a large class of one-parameter families of K3-surface fibered Calabi-Yau threefolds together with an explicit description of their periods. By a quadratic twist we construct models for moduli spaces of lattice polarized K3 surfaces of high Picard-rank such that their multi-parameter K3 periods can be computed explicitly. Restricting to sub-loci and carrying out another quadratic twist one obtains the desired one-parameter families of Calabi-Yau threefolds. The period computation makes essential use of a generalization of the classical Euler transform for the hypergeometric function. All symplectically rigid rank four differential operators of Calabi-Yau type are realized in this way. This is joint work with Andreas Malmendier.
Tuesday, November 25th, at 4:00pm in HBH 227
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