The cohomology of line bundles on Hopf manifolds (Q1197482)

The paper gives an elementary method for the computation of the cohomology groups \(H^ q(X,\Omega^ p(L))\), where \(X\) is a Hopf manifold and \(\Omega^ p(L)\) is the sheaf of germs of holomorphic \(p\)-forms with values in a holomorphic line bundle \(L\) on \(X\). The method is exposed first for flat line bundles. To prove the general case the author shows, extending a result of K. Kodaira for Hopf surfaces, that all line bundles on an arbitrary Hopf manifold are flat.