Advances in Theoretical and Mathematical Physics

Volume 16 (2012)

Number 3

Groups acting freely on Calabi–Yau threefolds embedded in a product of del Pezzo surfaces

Pages: 887 – 933

DOI: https://dx.doi.org/10.4310/ATMP.2012.v16.n3.a4

Authors

Gilberto Bini (Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy)

Filippo F. Favale (Dipartimento di Matematica, Università degli Studi di Pavia, Pavia, Italy)

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 groups of $X$, which is described in terms of the automorphism group of the two del Pezzo surfaces.

Published 7 February 2013