Invariance of cohomological \(q\)-completeness under finite holomorphic surjections
type: Item
instance of: scholarly article
title: Invariance of cohomological \(q\)-completeness under finite holomorphic surjections
zbMATH Open document ID: 0810.32012
DOI: 10.1007/BF02567691
author: Viorel Vâjâitu
published in: Manuscripta Mathematica
publication date: 1994-07-04T00:00:00Z
full work available at URL: https://eudml.org/doc/155921
review text: The following two results on the invariance of cohomologically \(q\)- completeness and cohomomological \(q\)-convexity are proven: Theorem 1. Let \(\pi : X \to Y\) be a finite surjective holomorphic map of finite dimensional reduced complex spaces. Then \(X\) is cohomologically \(q\)-complete (cohomologically \(q\)-convex) iff \(Y\) is cohomologically \(q\)- complete (cohomologically \(q\)-convex). Theorem 2. Let \(\pi : X \to Y\) be a holomorphic map of reduced complex spaces with \(Y\) finite dimensional. Suppose that: (i) \(\pi\) is a Stein morphism; (ii) There is a compact (topological) group \(G\) acting continuously on \(X\) (by holomorphic transformations) which preserves the fibers of \(\pi\). (iii) Any \(G\)-invariant holomorphic function on a fibre of \(\pi\) is constant. Then \(Y\) is cohomologically \(q\)-complete (cohomologically \(q\)-convex) if \(X\) is cohomologically \(q\)-complete (cohomologically \(q\)-convex).
Mathematics Subject Classification ID: 32F10
zbMATH DE Number: 599652
zbMATH Keywords: cohomologically \(q\)-completeness
zbMATH Keywords: \(q\)-convexity
zbMATH Keywords: surjective holomorphic map
zbMATH Keywords: complex spaces
reviewed by: Nicolae Mihalache
MaRDI profile type: Publication
cites work: Q3949289
cites work: Geometric invariant theory on Stein spaces
cites work: On the Invariance of q-Convexity and Hyperconvexity Under Finite Holomorphic Surjections
cites work: Certain cones are not set-theoretic complete intersections
description: scientific article; zbMATH DE number 599652