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 $F_G^A$ of Calabi-Yau 3-folds $A/G$ with A an abelian 3-fold and $G\le \text{Aut}\left(A\right)$ 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 $X\in F_G^A$. Additionally, we construct and classify the quotients $X/\Upsilon$ for any $\Upsilon \le \text{Aut}\left(X\right)$. Specifically, for those groups ϒ that preserve the volume form of X then $X/\Upsilon$ 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.