Calculating cohomology groups of moduli spaces of curves via algebraic geometry

1998/02/28 by Enrico Arbarello, Arbarello, Enrico, Maurizio Cornalba +1 · 4 citations
Mathematics · #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14H10

paper · pdf · doi:10.48550/arxiv.math/9803001

lamstex, 33 pages, 2 figures

arxiv created 1998/02/28 · openalex publication_date 1998/02/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the first, second, third, and fifth rational cohomology groups of the moduli space of stable n-pointed genus g curves, for all g and n, using (mostly) algebro-geometric techniques.

Citations

• Topological recursion relations in genus 2
• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves

Cited by

• Vanishing H¹ for Hurwitz spaces of fully-marked admissible covers of degree 3
• On O'Grady's generalized Franchetta conjecture for genus 11 K3 surfaces
• FA-modules of holomorphic forms on M_g,n
• Symmetric and non-symmetric F-conjectures are equivalent

Related

• On the cohomology of moduli spaces of (weighted) stable rational curves
• The moduli space of stable n-pointed curves of genus zero
• Divisors in the moduli spaces of curves
• Cohomology of moduli spaces of curves of genus three via point counts
• Cohomology of moduli spaces