The classification of automorphisms and quotients of Calabi-Yau threefolds of type A

Abstract

The aim of the paper is to investigate the only two families FGA of Calabi-Yau 3-folds A/G with A an abelian 3-fold and G≤Aut(A) a finite group acting freely: one is constructed in [11] and the other is presented here. We provide a complete classification of the automorphism group of X∈FGA. Additionally, we construct and classify the quotients X/ϒ for any ϒ≤Aut(X). Specifically, for those groups ϒ that preserve the volume form of X then X/ϒ admits a desingularization Y which is a Calabi-Yau 3-fold: we compute the Hodge numbers and the fundamental group of these Y, thereby determining all topological in-equivalent Calabi-Yau 3-folds obtained in this way.