On the residues of Baum-Bott
type: Item
instance of: scholarly article
title: On the residues of Baum-Bott
zbMATH Open document ID: 1207.32027
author: El Hadji Malick Dia
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2010-10-12T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/115883
review text: Consider a compact complex manifold \(V\) of complex dimension \(n\), a holomorphic vector field \(v\) on \(V\), a vector bundle \(E\) of rank \(r\) on \(V\), and a \(\mathbb{C}\)-action \(\theta_v\) on \(E\). If \(v\) has no singularities, the Chern numbers \(c_I(E)\cap [V]\) are zero. If \(v\) has singularities Bott has shown that the Chern numbers localize near these singularities. The author obtains some generalizations of the results of Bott and Baum-Bott. After presenting some definitions and known results, the author presents a proof for the existence of residues. Next he obtains a generalization for the case where \(v\) is degenerate along a holomorphic submanifold \(W\). First he obtains the residues by using a special covering (Theorem A). Then the covering is suitably modified in order to obtain Theorems B,C, and D. Some applications of the obtained results are presented.
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32M25
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 5799095
zbMATH Keywords: Chern numbers
zbMATH Keywords: residues
zbMATH Keywords: degenerate isolated point
zbMATH Keywords: degenerate holomorphic submanifold
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
OpenAlex ID: W1981760533
cites work: Q5589098
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DOI: 10.5802/AFST.1247
description: scientific article; zbMATH DE number 5799095