Smoothing q-convex functions in the singular case (Q1071906)

This article generalizes a previous paper by the same authors [Invent. Math. 82, 291-305 (1985; see the review above)) to any complex space. This leads to the following beautiful vanishing result: Theorem: Let \(A\subset {\mathbb{P}}^ n\) a closed algebraic subvariety of maximal codimension q, and let S be a coherent analytic sheaf on \({\mathbb{P}}^ n- A.\) If d is the dimension of the support of S, then \(H^ j({\mathbb{P}}^ n- A,S)=0\) for \(j\geq d-[\frac{d}{q}]+1.\)