Generalised Lelong-Poincar\'e formula in complex Bott-Chern cohomology
Xiaojun Wu
TL;DR
This paper provides a topological proof of a generalized Lelong-Poincaré formula, linking the top Chern class of a vector bundle to the cycle class of its zero locus in complex Bott-Chern cohomology.
Contribution
It introduces a topological proof of the generalized Lelong-Poincaré formula relating Chern classes and zero loci in complex Bott-Chern cohomology.
Findings
Topological proof of the generalized Lelong-Poincaré formula
Identification of the top Chern class with the cycle class of the zero locus
Application in complex Bott-Chern cohomology
Abstract
In this note, we present a topological proof of the generalized Lelong-Poincar\'e 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Advanced Algebra and Geometry