Finite quotients of abelian varieties with a Calabi-Yau resolution (Q6621567)

Let \(A\) be an abelian variety, and \(G \subset \text{Aut} (A)\) a finite group of automorphisms acting freely in codimension two. The author is interested whether the singular quotient \(A/G\), which is of purely abelian type in terms of the Beauville-Bogomolov decomposition, admits a resolution of singularities that is a Calabi-Yau manifold. The author classifies the possible abelian varieties \(A\) as above (up to isogeny) in any dimension. In particular, there are no new irreducible examples in dimension \(4\). The author conjectures there are no irreducible examples of dimension \(n \geq 5\) either. In the proofs the author uses various techniques including Yamagishi's criterion for certain quotient singularities to admit crepant resolutions, and some computer-assisted results from finite group theory.