2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72258A family of proper smooth curves of genus $\geq 2$, parametrised by an open dense subset $U$ of a normal variety $S$, extends to $S$ if the natural map $π_1(U) \to π_1(S)$ on fundamental groups is an isomorphism. The criterion of this note is actually more precise.12 pages; revised version including a section on outer representations for families of curvesAlgebraic Geometry14F35; 14H30text