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

The aim of the paper is to investigate the only two families of Calabi-Yau 3-folds with A an abelian 3-fold and 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 . Additionally, we construct and classify the quotients for any . Specifically, for those groups ϒ that preserve the volume form of X then 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.