A remark on the Douady sequence for non-primary Hopf manifolds
type: Item
instance of: scholarly article
title: A remark on the Douady sequence for non-primary Hopf manifolds
zbMATH Open document ID: 1068.32013
author: Xiangyu Zhou
published in: The Asian Journal of Mathematics
publication date: 2005-03-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ajm/1087840912
review text: A compact \(n\)-dimensional complex manifold \(X\) is called a Hopf manifold if its universal covering is biholomorphic to \(W:= \mathbb{C}^n\backslash \{0\}\). If \(X \cong W/Z\), then \(X\) is said to be primary. The Douady sequence is a short exact sequence of complexes. It was used to compute the cohomology groups of line bundles on primary Hopf manifolds. Here the author generalizes it to non-primary Hopf manifolds. He writes that this can be used to obtain a criterion for the existence of holomorphic structures on topological vector bundles on \(X\), the study of the filtrabilty of holomorphic vector bundles on \(X\) and the study of moduli spaces of vector bundles on \(X\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 32J18
Mathematics Subject Classification ID: 32L10
zbMATH DE Number: 2148245
zbMATH Keywords: Hopf manifold
zbMATH Keywords: primary Hopf manifold
zbMATH Keywords: Douady sequence
MaRDI profile type: Publication
OpenAlex ID: W2026116878
DOI: 10.4310/AJM.2004.V8.N1.A10
description: scientific article; zbMATH DE number 2148245