Groups Acting Freely on Calabi-Yau Threefolds Embedded in a Product of del Pezzo Surfaces

Abstract

In this paper, we investigate quotients of Calabi-Yau manifolds Y embedded in Fano varieties X which are products of two del Pezzo surfaces - with respect to groups G that act freely on Y. In particular, we revisit some known examples and we obtain some new Calabi-Yau varieties with small Hodge numbers. The groups G are subgroups of the automorphism group of X, which is described in terms of the automorphism group of the two del Pezzo surfaces.