On Threefolds Isogenous to a Product of Curves
  A threefold isogenous to a product of curves $X$ is a quotient of a product of three compact Riemann surfaces of genus at least two by the free action of a finite group. In this paper we study these threefolds under the assumption that the group acts diagonally on the product. We show that the classification of these threefolds is a finite problem, present an algorithm to classify them for a fixed value of $\chi(\mathcal O_X)$ and explain a method to determine their Hodge numbers. Running an implementation of the algorithm we achieve the full classification of threefolds isogenous to a product of curves with $\chi(\mathcal O_X)=-1$, under the assumption that the group acts faithfully on each factor. 
Davide Frapporti, Christian Gleissner
math.AG