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

TL;DR

This paper studies free group actions on Calabi-Yau threefolds embedded in products of del Pezzo surfaces, leading to new Calabi-Yau varieties with small Hodge numbers.

Contribution

It introduces new examples of Calabi-Yau threefolds obtained as quotients under free group actions, expanding the known landscape of such varieties.

Findings

Revisited known Calabi-Yau examples with group actions

Constructed new Calabi-Yau varieties with small Hodge numbers

Described automorphism groups of the ambient Fano varieties

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.