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<p>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 equals to the cycle class of the schematic zero locus of the section in complex Bott–Chern cohomology.</p>

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Generalised Lelong–Poincaré formula in complex Bott–Chern cohomology

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Xiaojun Wu

摘要

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 equals to the cycle class of the schematic zero locus of the section in complex Bott–Chern cohomology.