Cohomology with compact supports for cohomologicallyq-convex spaces

摘要

We show that if X is a complex space of dimension n which is cohomologically q-convex (resp., cohomologically q-complete), then $ H^{i}_{c} (X, mathbb{C}) $ is a finite dimensional vector space (resp., vanishes) for $ i leq nu_{q}(X)-q $, where the number $ nu_{q}(X) $ depends on the nature of singularities of X and equals n if X is smooth.