ABELIAN COVERS AND ISOTRIVIAL CANONICAL FIBRATIONS

Abstract

We give a pure algebraic method to construct all the infinite families of surfaces S with isotrivial canonical fibration where S is the minimal desingularization of X = Z/G and G is an Abelian group acting diagonally on the product of two smooth curves: Z = F × D. In particular we recover all the known infinite families of surfaces with isotrivial canonical fibration and we produce many new ones. Our method works in every dimension and, with minor modifications, it can be applied to construct surfaces with canonical map of degree > 1.

ACKNOWLEDGMENT

I would like to thank F. Catanese for pointing out some evidence [5] which brought me to theorem 2.3, then M. Manetti for showing me a short way to exclude the genus-5 case and the group of geometers of Dipartimento di Matematica del Politecnico di Torino, where I wrote the first version of this paper, for their supportive attitude. Research carried out under the project “Geometria Algebrica, Algebra Commutativa e aspetti comutazionali” (coordinatore nazionale Claudio Pedrini).