Some convexity properties of morphisms of complex spaces
type: Item
instance of: scholarly article
title: Some convexity properties of morphisms of complex spaces
zbMATH Open document ID: 0806.32006
DOI: 10.1007/BF02571943
author: Viorel Vâjâitu
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174689
review text: The following main theorem is proved: Theorem. Let \(\pi : X \to Y\) be a proper holomorphic map of finite dimensional complex spaces with at most \(r\)-dimensional fibres. Assume that \(Y\) is \(q\)-complete (in the sense of Andreotti and Grauert). Then \(X\) is \((q+r)\)-complete. The particular case when \(Y\) is 1-complete (in our normalization this corresponds to Stein spaces) answers a question raised by Okonek [see \textit{Chr. Okonek}, Lect. Notes Math. 1194, 104-126 (1986; Zbl 0593.32011)]. As an application a characterization theorem of \(q\)- completeness for holomorphically convex spaces follows. Namely: Theorem. Let \(X\) be a finite-dimensional holomorphically convex space. Then the following statements are equivalent: 1) \(X\) is \(q\)-complete; 2) \(X\) is cohomologically \(q\)-complete; 3) \(X\) does not contain compact analytic subsets of dimension \(\geq q\).
reviewed by: Viorel Vâjâitu
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32C15
zbMATH DE Number: 704947
zbMATH Keywords: \(q\)-complete
zbMATH Keywords: complex space
zbMATH Keywords: holomorphically convex spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 704947