Chow Stability of Curves of Genus 4 in P³

2008/06/04 by Hosung Kim, Ho‐Sung Kim, Kim, Hosung · 1 citation
Mathematics · #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14H10

paper · pdf · doi:10.48550/arxiv.0806.0731

This paper has been withdrawn by the author due to a crucial error

openalex publication_date 2008/06/04 · arxiv created 2010/08/30 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we study the GIT construction of the moduli space of Chow semistable curves of genus 4 in P³. By using the GIT method developed by Mumford and a deformation theoretic argument, we give a modular description of this moduli space. We classify Chow stable or Chow semistable curves when they are irreducible or nonreduced. Then we work out the case when a curve has two components. Our classification provides some clues to understand the birational map from the moduli space of stable curves of genus 4 to the moduli space of Chow semistable curves of genus 4 in P³.

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• Birational contraction of genus two tails in the moduli space of genus four curves I

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