On the cohomological completeness of {$q$}-complete domains with corners

Abstract

We prove the vanishing and non-vanishing theorems for an intersection of a finite number of $q$-complete domains in a complex manifold of dimension $n$. When $q$ does not divide $n$, it is stronger than the result naturally obtained by combining the approximation theorem of Diederich-Fornaess for $q$-convex functions with corners and the vanishing theorem of Andreotti-Grauert for $q$-complete domains. We also give an example which implies our result is best possible.