Classification of Bagnera-de Franchis Varieties in Small Dimensions

Abstract

A Bagnera-de Franchis variety $X=A/G$ is the quotient of an abelian variety $A$ by a free action of a finite cyclic group $G\subset Bihol(A)$, which does not contain only translations. Constructing explicit polarizations and using a method introduced by F. Catanese, we classify split Bagnera-de Franchis varieties up to complex conjugation in dimensions $\le 4$.

arXiv comment20 pages