Smooth contractible hypersurfaces in \(\mathbb{C}^ n\) and exotic algebraic structures on \(\mathbb{C}^ 3\)
type: Item
instance of: scholarly article
title: Smooth contractible hypersurfaces in \(\mathbb{C}^ n\) and exotic algebraic structures on \(\mathbb{C}^ 3\)
zbMATH Open document ID: 0792.57013
DOI: 10.1007/BF02572420
author: Shulim Kaliman
published in: Mathematische Zeitschrift
publication date: 1994-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/174584
review text: We present new examples of exotic algebraic structures on \(\mathbb{R}^ 6\), i.e., examples of smooth complex affine algebraic manifolds that are diffeomorphic to \(\mathbb{R}^ 6\), but not isomorphic to \(\mathbb{C}^ 3\). These exotic algebraic structures are contractible hypersurfaces in \(\mathbb{C}^ 4\), each of them admits a regular \(\mathbb{C}^*\)-action with one fixed point and they have Kodaira logarithmic dimension 2. We also present a general method of constructing contractible hypersurfaces in \(\mathbb{C}^ n\) which are not equivalent to a hyperplane up to a polynomial coordinate substitution.
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 567457
zbMATH Keywords: exotic algebraic structures
zbMATH Keywords: smooth complex affine algebraic manifolds
zbMATH Keywords: contractible hypersurfaces
zbMATH Keywords: Kodaira logarithmic dimension
MaRDI profile type: Publication
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OpenAlex ID: W2012420991
description: scientific article; zbMATH DE number 567457