2004/06/11 by Hubert Flenner, Mikhail Zaidenberg, Flenner, Hubert +1 · 2 citations
Mathematics · #14J50 #14R05 #14R20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AG #msc:14J50 #msc:14R05 #msc:14R20
paper · pdf · doi:10.48550/arxiv.math/0406239
11/06/2004 2 version 14/06/2004
openalex publication_date 2004/06/11 · arxiv created 2004/06/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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≤ 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 P1× \bf P1\backslash Δ, where Δ is the diagonal, and (d) V=\bf P2\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.