On a class of Danielewski surfaces in affine 3-space
| dc.creator | Dubouloz, Adrien | |
| dc.creator | Poloni, Pierre-Marie | |
| dc.date | 2006-02-24 | |
| dc.date | 2006-08-27 | |
| dc.date.accessioned | 2026-07-07T07:03:45Z | |
| dc.date.available | 2026-07-07T07:03:45Z | |
| dc.description | L. Makar-Limanov computed the automorphisms groups of surfaces in $\mathbb{C}^{3}$ defined by the equations $x^{n}z-P(y)=0$, where $n\geq1$ 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 $n\geq2$ 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 $n\geq2$ 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 $\mathbb{C}^{3}$. | |
| dc.description | Revised version with simplified proofs. A classification of special Danielewski surfaces admitting multiplicative group actions has been added | |
| dc.identifier | https://arxiv.org/abs/math/0602549 | |
| dc.identifier | http://arxiv.org/abs/math/0602549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109095 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14R10, 14R05 | |
| dc.title | On a class of Danielewski surfaces in affine 3-space | |
| dc.type | text |