Residue currents of cohesive modules and the generalized Poincaré-Lelong formula on complex manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916421409177600 |
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| author | Wei, Zhaoting |
| author_facet | Wei, Zhaoting |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Residue currents of cohesive modules and the generalized Poincaré-Lelong formula on complex manifolds Wei, Zhaoting Algebraic Geometry Complex Variables Differential Geometry 2020: 32C30, 32A27, 14F08, 32J25 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. |
| title | Residue currents of cohesive modules and the generalized Poincaré-Lelong formula on complex manifolds |
| topic | Algebraic Geometry Complex Variables Differential Geometry 2020: 32C30, 32A27, 14F08, 32J25 |
| url | https://arxiv.org/abs/2409.17362 |