Fibrations of low genus, I
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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.
50 pages, to appear on Annales Scientifiques de l'Ecole Normale Superieure
50 pages, to appear on Annales Scientifiques de l'Ecole Normale Superieure