Fibrations of low genus, I

2005/03/15 by Catanese, Fabrizio, Pignatelli, Roberto
#11G30 #14D06 #14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0503294

Abstract

In the present paper we consider fibrations f: S \ra B of an algebraic surface onto a curve B, with general fibre a curve of genus g. Our main results are: 1) A structure theorem for such fibrations in the case g=2 2) A structure theorem for such fibrations in the case g=3 and general fibre nonhyperelliptic 3) A theorem giving a complete description of the moduli space of minimal surfaces of general type with K²_S = 3, p_g = q=1, showing in particular that it has four unirational connected components 4) some other applications of the two structure theorems.

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