Cohomological q-convexity versus local q-completeness with corners
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We show that if (D, π) is an unramified Riemann domain over a distinguished complex manifold X such that D is cohomologically q-convex, then π is locally q-complete with corners. We call X distinguished if for every point x of X there is a holomorphic line bundle \(\cal L\) on X (which may depend on x) so that the global sections \(\Gamma (X \cal L)\) of \(\cal L\) generate its 1-jets at x. Examples of distinguished complex manifolds include all complex submanifolds of Cm × Pn; in particular all Stein or projectively algebraic manifolds.
Key wordsUnramified Riemann domains q-convexity functions q-convex with corners
Mathematics Subject Classification (1991)32 F 10
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