A monodromy criterion for extending curves

2004/08/23 by Jakob Stix, Stix, Jakob · 2 citations
Computer Science · Mathematics · #14F35 #14H30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation #math.AG #msc:14F35 #msc:14H30

paper · pdf · doi:10.48550/arxiv.math/0408315

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

openalex publication_date 2004/08/23 · arxiv created 2004/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A family of proper smooth curves of genus ≥ 2, parametrised by an open dense subset U of a normal variety S, extends to S if the natural map π₁(U) → π₁(S) on fundamental groups is an isomorphism. The criterion of this note is actually more precise.

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• Families of curves separating points
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