Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients

2023/03/31 by Matteo Costantini, Martin Möller, Costantini, Matteo +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2303.17929

openalex publication_date 2023/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We provide formulas for the Chern classes of linear submanifolds of the moduli spaces of Abelian differentials and hence for their Euler characteristic. This includes as special case the moduli spaces of k-differentials, for which we set up the full intersection theory package and implement it in the sage-program diffstrata. As an application, we give an algebraic proof of the theorems of Deligne-Mostow and Thurston that suitable compactifications of moduli spaces of k-differentials on the 5-punctured projective line with weights satisfying the INT-condition are quotients of the complex two-ball.

Cited by

• Finite isoresidual covers in strata of k-differentials

Related

• The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials
• The area is a good enough metric
• Chern classes on differential K-theory
• Intersection theory and Chern classes in Bott-Chern cohomology
• Remarks on the Chern classes of Calabi-Yau moduli