A monodromy criterion for extending curves

Details A monodromy criterion for extending curves A monodromy criterion for extending curves

2004-08-23

arxiv.org/abs/math/0408315v2

Mathematics

Algebraic Geometry

12 pages; revised version including a section on outer representations for families of curves

Scientific paper

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
$\pi_1(U) \to \pi_1(S)$ on fundamental groups is an isomorphism. The criterion
of this note is actually more precise.

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