Fibered neighborhoods of curves in surfaces
type: Item
instance of: scholarly article
title: Fibered neighborhoods of curves in surfaces
zbMATH Open document ID: 1036.32009
DOI: 10.1007/BF02930996
published in: The Journal of Geometric Analysis
publication date: 2003-12-04T00:00:00Z
review text: Let \(M\) a smooth two-dimensional complex manifold and \(S \subset X\) a smooth compact Riemann surface of genus \(g\). Here the authors prove that if the normal bundle \(N_S\) of \(S\) in \(M\) has degree \(S\cdot S \leq 3-2g\), then a small neighborhood of \(S\) in \(M\) is fibered equivalent (and in particular biholomorphic) to a neighborhood of \(S\) in \(N_S\). For a very good introduction and many interesting results in the higher dimensional case, see the e-print [\textit{C. Camacho} and \textit{H. Movasati}, Neighborhoods of analytic varieties in complex manifolds, arXiv: math.CV/0208058].
Mathematics Subject Classification ID: 32E05
Mathematics Subject Classification ID: 32L20
Mathematics Subject Classification ID: 32F32
Mathematics Subject Classification ID: 32C22
zbMATH DE Number: 2013175
zbMATH Keywords: holomorphic fibrations
zbMATH Keywords: Serre duality
zbMATH Keywords: holomorphically convex neighborhood of curves
zbMATH Keywords: normal bundle
author: César Camacho
author: Hossein Movasati
author: Paulo Sad
reviewed by: E. Ballico
MaRDI profile type: Publication
cites work: Q3903276
cites work: Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves
cites work: Invariant varieties through singularities of holomorphic vector fields
cites work: Dicritical singularities of holomorphic vector fields
cites work: Über Modifikationen und exzeptionelle analytische Mengen
cites work: Q5565313
cites work: Normal Two-Dimensional Singularities. (AM-71)
description: scientific article; zbMATH DE number 2013175