Holomorphic Koszul-Brylinski homologies of Poisson blow-ups

2022/02/20 by Xiaojun Chen, Youming Chen, Chen, Xiaojun +5
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2202.09764

openalex publication_date 2022/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a blow-up formula for holomorphic Koszul-Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the E₁-degeneracy of the Dolbeault-Koszul-Brylinski spectral sequence under Poisson blow-ups, and compute the holomorphic Koszul-Brylinski homology for del Pezzo surfaces and two complex nilmanifolds with holomorphic Poisson structures.

Related

• Holomorphic Poisson Cohomology
• Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds
• Degeneracy of Holomorphic Poisson Spectral Sequence
• The homology theory of Koszul-Vinberg algebroids and Poisson manifolds II
• Deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes