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A monodromy criterion for extending curves

Jakob Stix
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Abstract

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.

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Jakob Stix. 2004-11-10. A monodromy criterion for extending curves. https://arxiv.org/abs/math/0408315

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