Mathematics – Algebraic Geometry
Scientific paper
2004-06-11
Mathematics
Algebraic Geometry
11/06/2004 2 version 14/06/2004
Scientific paper
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) $V={\bf P}^1\times {\bf P}^1\backslash \Delta$, where $\Delta$ 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.
Flenner Hubert
Zaidenberg Mikhail
No associations
LandOfFree
On the uniqueness of ${\bf C}^*$-actions on affine surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the uniqueness of ${\bf C}^*$-actions on affine surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the uniqueness of ${\bf C}^*$-actions on affine surfaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-106546