Moduli stack of stable curves from a stratified homotopy viewpoint

2023/08/18 by Mikala Ørsnes Jansen, Jansen, Mikala Ørsnes · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2308.09551

openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1984, Charney and Lee defined a category of stable curves and exhibited a rational homology equivalence from its geometric realisation to (the analytification of) the moduli stack of stable curves, also known as the Deligne-Mumford-Knudsen compactification. We strengthen this result by showing that, in fact, this category captures the stratified homotopy type of the moduli stack. In particular, it classifies constructible sheaves via an exodromy equivalence.

Cited by

• Localizing invariants of constructible sheaves

Related

• One-dimensional substacks of the moduli stack of Deligne-Mumford stable curves
• The one-dimensional stratum in the boundary of the moduli stack of stable curves
• Stable maps to quotient stacks with a properly stable point
• Complete moduli for fibered surfaces
• Notes on the construction of the moduli space of curves