The one-dimensional stratum in the boundary of the moduli stack of stable curves

2007/12/27 by Joerg Zintl, Zintl, Joerg
Mathematics · #14H10 (Primary) 14H37 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0712.4251

openalex publication_date 2007/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The moduli stack of Deligne-Mumford stable curves of genus g admits a stratification, so that the number of nodes of the curves belonging to one stratum is constant. The irreducible components of the stratum corresponding to curves with exactly 3g-4 nodes are one-dimensional substacks. We show how they can be related to moduli stacks of (permutation classes of) pointed stable curves. Using this, we construct all components of this stratum in a new way as quotient stacks.

Related

• One-dimensional substacks of the moduli stack of Deligne-Mumford stable curves
• Moduli stacks of permutation classes of pointed stable curves
• Moduli stacks of curves with a fixed dual graph
• Complete moduli for fibered surfaces
• Moduli stack of stable curves from a stratified homotopy viewpoint