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2000 Invariant subvarieties of low codimension in the affine spaces
Kayo Masuda, Masayoshi Miyanishi
Tohoku Math. J. (2) 52(1): 61-77 (2000). DOI: 10.2748/tmj/1178224658

Abstract

Let $W$ be an irreducible subvariety of codimension $r$ in a smooth affine variety $X$ of dimension $n$ defined over the complex field $C$. Suppose that $W$ is left pointwise fixed by an automorphism of $X$ of infinite order or by a one-dimensional algebraic torus action on $X$. In the present article, we consider whether or not $X$ is then an affine space bundle over $W$ of fiber dimension $n-r$. Our results concern the case $r=1$ or the case $r=2$ and $n\leq3$. As by-products, we obtain algebro-topological characterizations of the affine 3-space.

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Kayo Masuda. Masayoshi Miyanishi. "Invariant subvarieties of low codimension in the affine spaces." Tohoku Math. J. (2) 52 (1) 61 - 77, 2000. https://doi.org/10.2748/tmj/1178224658

Information

Published: 2000
First available in Project Euclid: 3 May 2007

zbMATH: 0972.14038
MathSciNet: MR1740543
Digital Object Identifier: 10.2748/tmj/1178224658

Subjects:
Primary: 14R05
Secondary: 14J70

Rights: Copyright © 2000 Tohoku University

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