On Threefolds Isogenous to a Product of Curves

2014/12/19 by Frapporti, Davide, Gleissner, Christian · 1 citation
#14J30 #14L30 #14Q99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.6365

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 χ(\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 χ(\mathcal O_X)=-1, under the assumption that the group acts faithfully on each factor.

Cited by

• Pluricanonical Geometry of Varieties Isogenous to a Product and Abelian Covers

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