The Runge approximation problem for holomorphic maps into Grassmannians
type: Item
instance of: scholarly article
title: The Runge approximation problem for holomorphic maps into Grassmannians
zbMATH Open document ID: 0827.32015
DOI: 10.1007/BF02571908
published in: Mathematische Zeitschrift
publication date: 1995-07-26T00:00:00Z
full work available at URL: https://eudml.org/doc/174733
review text: Let \(X\) be a complex affine algebraic variety and let \(f : X \to \mathbb{G}_{n, p}\) be a holomorphic map into the Grassmannian of \(p\)- dimensional complex vector subspaces of \(\mathbb{C}^n\). Assume that \(p + \dim X \leq n\). It is proved that \(f\) can be approximated by regular maps (that is, algebraic morphisms) if and only if the pull-back vector bundle \(f^* \gamma_{n,p}\), where \(\gamma_{n,p}\) is the universal vector bundle on \(\mathbb{G}_{n,p}\), admits an algebraic structure. Some applications are also discussed.
Mathematics Subject Classification ID: 32E30
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 778949
zbMATH Keywords: Runge approximation
zbMATH Keywords: holomorphic maps
zbMATH Keywords: complex affine algebraic variety
zbMATH Keywords: Grassmannian
author: Wojciech Kucharz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 778949