Residue currents of cohesive modules and the generalized Poincaré-Lelong formula on complex manifolds

2024/09/25 by Zhaoting Wei, Wei, Zhaoting
Mathematics · #14F08 #2020: 32C30 #32A27 #32J25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2409.17362

openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cohesive module provides a tool to study coherent sheaves on complex manifolds by global analytic methods. In this paper we develop the theory of residue currents for cohesive modules on complex manifolds. In particular we prove that they have the duality principle and satisfy the comparison formula. As an application, we prove a generalized version of the Poincaré-Lelong formula for cohesive modules, which applies to coherent sheaves without globally defined locally free resolutions.

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