A monodromy criterion for extending curves

Abstract

A family of proper smooth curves of genus $\ge 2$, parametrised by an open dense subset $U$ of a normal variety $S$, extends to $S$ if the natural map ${\pi }_1(U)\to {\pi }_1(S)$ 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 curves