On sections with isolated singularities of twisted bundles and applications to foliations by curves
type: Item
instance of: scholarly article
title: On sections with isolated singularities of twisted bundles and applications to foliations by curves
zbMATH Open document ID: 1046.32008
author: Jorge Olivares
author: Antonio Campillo
published in: Mathematical Research Letters
publication date: 2004-05-18T00:00:00Z
review text: The authors prove two main results: Let \(M\) be a compact Kähler manifold of an ample line bundle \(L\rightarrow M\), and let \(E\rightarrow M\) be a holomorphic vector bundle of rank \(n=\dim M\geq 2\). There exists an integer \(r_0\) such that \(s'=\varphi(s)\) for some endomorphism of \(E\), if \(s, s'\) are two global sections of \(E\otimes L^{\otimes r} (r\geq r_0)\) such that \(s\) has isolated zeros, and such that the closed subscheme of the zero set of \(s'\) contains that of the zero set of \(s\). The above theorem result is valid for \(r_0=1\) and \(n\geq2\), when \(L\) and \(E\) are the hyperplane and tangent bundles of \(\mathbb P^n\) respectively.
reviewed by: Xianghong Gong
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32L10
zbMATH DE Number: 2064721
zbMATH Keywords: compact projective manifold
zbMATH Keywords: holomorphic foliation by curves
zbMATH Keywords: section with isolated singularities
MaRDI profile type: Publication
full work available at URL: mrl.2003.v10.n5.a8
OpenAlex ID: W1494035333
DOI: 10.4310/MRL.2003.V10.N5.A8
description: scientific article; zbMATH DE number 2064721