2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101130In 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 SuperieureAlgebraic Geometry14D06; 14J29; 11G30text