Abstract
In the present paper we consider fibrations f : S → B of an algebraic surface over 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 where g = 2 . (2) A structure theorem for such fibrations in the case where g = 3 , the general fibre is nonhyperelliptic, and each fibre is 2-connected. (3) A theorem giving a complete description of the moduli space of minimal surfaces of general type with p g = q = 1 , K S 2 = 3 , showing in particular that it has four unirational connected components. (4) Other applications of the two structure theorems.
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