Generalised Lelong-Poincaré formula in complex Bott-Chern cohomology
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913527263920128 |
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| author | Wu, Xiaojun |
| author_facet | Wu, Xiaojun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Lelong-Poincaré formula in complex Bott-Chern cohomology Wu, Xiaojun Algebraic Geometry Complex Variables 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. |
| title | Generalised Lelong-Poincaré formula in complex Bott-Chern cohomology |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2410.01634 |