A monodromy criterion for extending curves
Abstract
Description
A 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 curves
12 pages; revised version including a section on outer representations for families of curves