2002/10/10 by Hubert Flenner, Mikhail Zaidenberg, Flenner, Hubert +1
Mathematics · #13A02 #13F15 #14L30 #14R05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AC #math.AG #msc:13A02 #msc:13F15 #msc:14L30 #msc:14R05
paper · pdf · doi:10.48550/arxiv.math/0210153
Uses P.Taylor's diagrams.tex
arxiv created 2002/10/10 · openalex publication_date 2002/10/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classification of normal affine surfaces admitting a \bf C^*-action was given in the work of Białynicki-Birula, Fieseler and L. Kaup, Orlik and Wagreich, Rynes and others. We provide a simple alternative description of such surfaces in terms of their graded rings as well as by defining equations. This is based on a generalization of the Dolgachev-Pinkham-Demazure construction in the case of a hyperbolic grading. As an apllication we determine the structure of singularities, of the orbits and the divisor class groups for such surfaces.