Cohomology of q-convex spaces in top degrees. (English) Zbl 0682.32017

It is shown that every strongly q-complete subvariety of a complex analytic space has a fundamental system of strongly q-complete neighborhoods. As a consequence, we find a simple proof of Ohsawa’s result that every non compact irreducible n-dimensional analytic space is strongly n-convex. An elementary proof of the existence of Hodge decomposition in top degrees for absolutely q-convex manifolds is also given.
Reviewer: J.P.Demailly


32F10 \(q\)-convexity, \(q\)-concavity
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