On the uniqueness of ${\bf C}^*$-actions on affine surfaces
| dc.creator | Flenner, Hubert | |
| dc.creator | Zaidenberg, Mikhail | |
| dc.date | 2004-06-11 | |
| dc.date | 2004-06-14 | |
| dc.date.accessioned | 2026-07-07T05:09:10Z | |
| dc.date.available | 2026-07-07T05:09:10Z | |
| dc.description | We prove that a normal affine surface $V$ over $\bf C$ admits an effective action of a maximal torus ${\bf T}={\bf C}^{*n}$ ($n\le 2$) such that any other effective ${\bf C}^*$-action is conjugate to a subtorus of $\bf T$ in Aut $(V)$, in the following particular cases: (a) the Makar-Limanov invariant ML$(V)$ is nontrivial, (b) $V$ is a toric surface, (c) $V={\bf P}^1\times {\bf P}^1\backslash Δ$, where $Δ$ is the diagonal, and (d) $V={\bf P}^2\backslash Q$, where $Q$ is a nonsingular quadric. In case (a) this generalizes a result of Bertin for smooth surfaces, whereas (b) was previously known for the case of the affine plane (Gutwirth) and (d) is a result of Danilov-Gizatullin and Doebeli. | |
| dc.description | 11/06/2004 2 version 14/06/2004 | |
| dc.identifier | https://arxiv.org/abs/math/0406239 | |
| dc.identifier | http://arxiv.org/abs/math/0406239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71533 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14R05, 14R20, 14J50 | |
| dc.title | On the uniqueness of ${\bf C}^*$-actions on affine surfaces | |
| dc.type | text |