Holomorphic vector bundle on Hopf manifolds with Abelian fundamental groups. (English) Zbl 1060.32006
Let \(X\) be a Hopf manifold with Abelian fundamental group and \(E\) a rank \(r\) holomorphic vector bundle on \(X\) with trivial pull-back to the universal covering \(W:= C^n\backslash \{0\}\) of \(X\).
Here the authors prove the existence of a line bundle \(L\) on \(X\) such that \(E\otimes L\) has a nowhere vanishing section and study the vector bundles filtrations of \(E\). D. Mall in [Math. Ann. 294, No. 4, 719–740 (1992; Zbl 0756.32018)] did the case in which \(X\) is primary, i.e \(\pi _1(X) \cong Z\).
Here the authors prove the existence of a line bundle \(L\) on \(X\) such that \(E\otimes L\) has a nowhere vanishing section and study the vector bundles filtrations of \(E\). D. Mall in [Math. Ann. 294, No. 4, 719–740 (1992; Zbl 0756.32018)] did the case in which \(X\) is primary, i.e \(\pi _1(X) \cong Z\).
Reviewer: Edoardo Ballico (Povo)
Keywords:
Hopf manifold; holomorphic vector bundle; \(n\)-dimensional Hopf manifold; Hopf manifold with Abelian fundamental groupCitations:
Zbl 0756.32018References:
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