Some mirror partners with complex multiplication

In this note we give examples of families of Calabi–Yau 3-manifolds over Shimura varieties, whose mirror families contain subfamilies over Shimura varieties. In the case of these families we obtain dense sets of complex multiplication fibers by using the fact that the base space is a Shimura variety. In view of the work of Gukov and Vafa [7] this is of special interest in theoretical physics.

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Published 1 January 2010