Residues of holomorphic vector fields relative to singular invariant subvarieties
type: Item
instance of: scholarly article
title: Residues of holomorphic vector fields relative to singular invariant subvarieties
zbMATH Open document ID: 0844.32007
author: Daniel Lehmann
author: Tatsuo Suwa
published in: Journal of Differential Geometry
publication date: 1996-09-08T00:00:00Z
review text: Let \(V\) be a locally complete intersection subspace of a complex manifold \(W\). Assume that the normal bundle \(N\), originally defined only on \(V\), extends to a smooth vector bundle defined in a neighbourhood of \(V\) in \(W\). Let \(F\) be a holomorphic foliation (with possible singularities) which leaves \(V\) invariant. The main results of the paper deal with explicit computations of the residues of the characteristic forms of the triple \((F, V,N)\). The proofs use the Chern-Weil formalism and a detailed local analysis of the differential geometric data. Prior related results of Baum and Bott are thus extended to subspaces with singularities. [See \textit{P. Baum} and \textit{R. Bott}, `On the zeroes of holomorphic vector fields', Essays Topol. Relat. Top. 29-47 (1970; Zbl 0193.52201) and J. Differ. Geom. 7, 279-342 (1972; Zbl 0268.57011)].
reviewed by: Mihai Putinar
Mathematics Subject Classification ID: 32A27
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 844217
zbMATH Keywords: locally complete intersection
zbMATH Keywords: holomorphic foliation
zbMATH Keywords: residue
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214457035
OpenAlex ID: W1513947990
Wikidata QID: Q115177956
DOI: 10.4310/JDG/1214457035
description: scientific article; zbMATH DE number 844217