Variation of the Green function on Riemann surfaces and Whitney's holomorphic stratification conjecture
type: Item
instance of: scholarly article
title: Variation of the Green function on Riemann surfaces and Whitney's holomorphic stratification conjecture
zbMATH Open document ID: 0735.30039
DOI: 10.1007/BF02698545
author: Robert Hardt
author: Dennis Sullivan
published in: Publications Mathématiques
publication date: 1992-06-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104034
review text: Let \(M\) be a Riemann surface. In this work, the authors study how the Green function on \(M\) varies when the conformal structure changes. Making use of this, the authors deal with the Whitney's conjecture for complex projective algebraic varieties making use of an interpolation formula of H. Whitney and proving that: Any complex algebraic subvariety of \(\mathbb{C}\mathbb{P}^ n\) admits a finite partition (stratification) \({\mathcal S}\) into holomorphic submanifolds such that, for each \(S\) in \({\mathcal S}\), every point of \(S\) has a neighborhood in \(\mathbb{C}\mathbb{P}^ n\) that may be foliated by \((\dim S)\)-dimensional holomorphic leaves that respect the strata.
Mathematics Subject Classification ID: 30F15
Mathematics Subject Classification ID: 32C25
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 32E30
zbMATH DE Number: 3971
zbMATH Keywords: finite partition into holomorphic submanifolds
zbMATH Keywords: interpolation
zbMATH Keywords: Riemann surface
zbMATH Keywords: Green function
zbMATH Keywords: Whitney's conjecture
zbMATH Keywords: stratification
Wikidata QID: Q123026598
reviewed by: Emilio Bujalance
MaRDI profile type: Publication
cites work: Q5515607
cites work: Topological Properties of Subanalytic Sets
cites work: Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings
cites work: Q3935870
description: scientific article; zbMATH DE number 3971