Generalised Lelong-Poincaré formula in complex Bott-Chern cohomology
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.01634
- arXiv:
- arXiv:2410.01634
- Bibcode:
- 2024arXiv241001634W
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Complex Variables
- E-Print:
- 11 pages