Fibrations of low genus, I
  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 $ K^2_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. 
Fabrizio Catanese (Universitaet Bayreuth), Roberto Pignatelli   (Universita' di Trento)