Invariant subvarieties of low codimension in the affine spaces

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概要

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• Let $W$ be an irreducible subvariety of codimension $r$ in a smooth affine variety $X$ of dimension $n$ defined over the complex field $\textbf{\textit{C}}$. 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.

• 東北大学の論文

著者

• MIYANISHI Masayoshi

  Department of Mathematics Graduate School of Science Osaka University

• Miyanishi Masayoshi

  Department Of Mathematics Faculty Of Science Osaka University

• Masuda Kayo

  Department of Mathematics, Himeji Institute of Technology

• Masuda Kayo

  Department Of Mathematics Himeji Institute Of Technology

関連論文

• Equivariant classification of Gorenstein open log del Pezzo surfaces with finite group actions
• Invariant subvarieties of low codimension in the affine spaces
• On contractible curves in the complex affine plane
• Logarithmic del Pezzo surfaces of rank one with non-contractible boundaries
• Unirational quasi-elliptic surfaces

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