A polar de Rham theorem
type: Item
instance of: scholarly article
title: A polar de Rham theorem
zbMATH Open document ID: 1060.14013
author: Alexei Rosly
author: Boris Khesin
author: Richard P. Thomas
published in: Topology
publication date: 2004-09-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0305081
review text: For a complex manifold \(X\) one can define its polar homology \(HP_*(X)\) as the homology of the polar chain complex whose building blocks are pairs \((Y,\beta)\) with \(Y\) a subvariety in \(X\) and \(\beta\) a meromorphic top degree form on \(Y\) having a simple pole. For \(X\) projective, the authors identify the group \(HP_q (X)\) with the Dolbeault cohomology group \(H^{n,n-q} (X)\) for all integers \(q\). A relative version for a pair \((X,D)\) with \(D\) a normal crossing divisor in \(X\) is also obtained.
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 58A14
zbMATH DE Number: 2102622
zbMATH Keywords: meromorphic forms
zbMATH Keywords: Poincaré residue
zbMATH Keywords: polar chain complex
reviewed by: Alexandru Dimca
MaRDI profile type: Publication
OpenAlex ID: W2097040859
arXiv ID: math/0305081
DOI: 10.1016/J.TOP.2004.01.001
description: scientific article