A remark on the Douady sequence for non-primary Hopf manifolds
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 \(X\).
scientific article; zbMATH DE number 2148245