On the Dolbeault Cohomology of Configuration Spaces

2025/09/05 by Peng Yang, Yang, Peng
Mathematics · #14F43 #32Q99 #55R80 #55T99 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.04756

openalex publication_date 2025/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Dolbeault cohomology ring of the configuration spaces of ℂⁿ and construct a spectral sequence that converges to the Dolbeault cohomology ring of the configuration spaces of an arbitrary complex manifold.

Related

• Dolbeault cohomology for almost complex manifolds
• The cohomology ring away from 2 of configuration spaces on real projective spaces
• Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology
• Dolbeault cohomologies of blowing up complex manifolds
• Dolbeault cohomology of nilmanifolds with left-invariant complex structure