Fibrations of low genus, I

In this paper we consider fibrations f of an algebraic surface S 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= 3, pg = q=1, showing in particular that it has four unirational connected components; 4) some other applications of the two structure theorems.