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- W2952030296 abstract "L. Makar-Limanov computed the automorphisms groups of surfaces in $mathbb{C}^{3}$ defined by the equations $x^{n}z-P(y)=0$, where $ngeq1$ and $P(y)$ is a nonzero polynomial. Similar results have been obtained by A. Crachiola for surfaces defined by the equations $x^{n}z-y^{2}-h(x)y=0$, where $ngeq2$ and $h(0)neq0$, defined over an arbitrary base field. Here we consider the more general surfaces defined by the equations $x^{n}z-Q(x,y)=0$, where $ngeq2$ and $Q(x,y)$ is a polynomial with coefficients in an arbitrary base field $k$. Among these surfaces, we characterize the ones which are Danielewski surfaces and we compute their automorphism groups. We study closed embeddings of these surfaces in affine 3-space. We show that in general their automorphisms do not extend to the ambient space. Finally, we give explicit examples of $mathbb{C}^{*}$-actions on a surface in $mathbb{C}^{3}$ which can be extended holomorphically but not algebraically to a $mathbb{C}^{*}$-action on $mathbb{C}^{3}$." @default.
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- W2952030296 date "2006-08-26" @default.
- W2952030296 modified "2023-09-25" @default.
- W2952030296 title "On a class of Danielewski surfaces in affine 3-space" @default.
- W2952030296 hasPublicationYear "2006" @default.
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