On Threefolds Isogenous to a Product of Curves

Davide Frapporti; Christian Gleissner

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arXiv · 1412.6365

On Threefolds Isogenous to a Product of Curves

Davide Frapporti·Christian Gleissner

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Abstract

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.

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Davide Frapporti, Christian Gleissner. 2014-12-19. On Threefolds Isogenous to a Product of Curves. https://arxiv.org/abs/1412.6365

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