Communications in Number Theory and Physics
Volume 4 (2010)
Some mirror partners with complex multiplication
Pages: 597 – 607
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  this is of special interest in theoretical physics.