q-completeness of subsets in complex projective space
type: Item
instance of: scholarly article
title: q-completeness of subsets in complex projective space
zbMATH Open document ID: 0611.32008
DOI: 10.1007/BF01161771
author: Mathias Peternell
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183707
review text: Let A be a q-codimensional algebraic submanifold of complex projective space. It is proved that \({\mathbb{P}}_ n-A\) is (2q-1)-complete. This implies a vanishing theorem for analytic cohomology groups and the Lefschetz theorem of Larsen on the homotopy of the pair \(({\mathbb{P}}_ n,A).\) Furthermore it is proved that on each open relatively compact subset of a manifold \({\mathbb{P}}_ n-B\) there exists a q-convex function, where B is an algebraic subset of \({\mathbb{P}}_ n\) with \(\dim B=n-q\) and arbitrary singularities. The theorem then follows from the q-convexity of \({\mathbb{P}}_ n-A\) for smooth A.
Mathematics Subject Classification ID: 32C25
Mathematics Subject Classification ID: 32L20
Mathematics Subject Classification ID: 32F10
zbMATH DE Number: 3987661
zbMATH Keywords: algebraic submanifold of complex projective space
zbMATH Keywords: vanishing theorem
zbMATH Keywords: q- convexity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3987661