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Type: Journal article
Title: Approximation and interpolation of regular maps from affine varieties to algebraic manifolds
Author: Larusson, F.
Truong, T.
Citation: Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci, 2019; 125(1-2):199-209
Publisher: Mathematica Scandinavica
Issue Date: 2019
ISSN: 0025-5521
Statement of
Finnur Larusson, Tuyen Trung Truong
Abstract: We consider the analogue for regular maps from affine varieties to suitable algebraic manifolds of Oka theory for holomorphic maps from Stein spaces to suitable complex manifolds. The goal is to understand when the obstructions to approximation or interpolation are purely topological. We propose a definition of an algebraic Oka property, which is stronger than the analytic Oka property. We review the known examples of algebraic manifolds satisfying the algebraic Oka property and add a new class of examples: smooth nondegenerate toric varieties. On the other hand, we show that the algebraic analogues of three of the central properties of analytic Oka theory fail for all compact manifolds and manifolds with a rational curve; in particular, for projective manifolds.
Rights: © 2019. This work is published under (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DOI: 10.7146/math.scand.a-114893
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