The cohomology of line bundles on non-primary Hopf manifolds
A Hopf manifold \(X\) is an \(n\)-dimensional compact complex manifold with \(W:= \mathbb {C}^n \backslash \{0\}\) as universal covering. Hence \(X = W/G\) with \(G\) a group. \(X\) is called primary if \(G = \mathbb {Z}\). Here the authors give an elementary method to compute the cohomology groups \(H^q(X,\Omega ^p_X(L))\), \(L\) a flat holomorphic line bundle, generalizing the case \(G = \mathbb {Z}\) done in [\textit{X. Y. Zhou}, Asian J. Math. 8, No. 1, 131--136 (2004; Zbl 1068.32013)] and the case \(G\) Abelian done in [\textit{X. Y. Zhou} and \textit{W. M. Liu}, Acta Math. Sin., Engl. Ser. 20, No. 4, 605--612 (2004; Zbl 1060.32006)].
scientific article; zbMATH DE number 5162305