Generalised Lelong-Poincaré formula in complex Bott-Chern cohomology

2024/10/02 by Xiaojun Wu, Wu, Xiaojun
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2410.01634

openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we present a topological proof of the generalized Lelong-Poincaré formula. More precisely, when the zero locus of a section has a pure codimension equal to the rank of a holomorphic vector bundle, the top Chern class of the vector bundle corresponds to the cycle class of the schematic zero locus of the section in complex Bott-Chern cohomology.

Related

• A generalized Poincaré-Lelong formula
• Intersection theory and Chern classes in Bott-Chern cohomology
• Bott-Chern homology, Bott-Chern differential cohomology and the Hodge conjecture
• Poincaré-Lelong type formulas and Segre numbers
• Construct holomorphic invariants in Čech cohomology by a combinatorial formula