Abstract
We prove a separation criterion for the compactly supported Dolbeault cohomology. As an application we give a simple proof of the following result: If X is an ( n− q)-convex complex manifold of dimension n, 1≤q≤n−1 , and K is a compact subset of X which admits a basis of q-convex neighborhoods, then H p, n− q ( X\\ K, E) is separated for all p and each holomorphic vector bundle E over X.
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