2005/11/10 by Hubert Flenner, Shulim Kaliman, Flenner, Hubert +3
Mathematics · #14J50 #14R05 #14R20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14J50 #msc:14R05 #msc:14R20
paper · pdf · doi:10.48550/arxiv.math/0511282
37 pages
arxiv created 2005/11/10 · openalex publication_date 2005/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Following an approach of Dolgachev, Pinkham and Demazure, we classified in math.AG/0210153 normal affine surfaces with hyperbolic \C*-actions in terms of pairs of \Q-divisors (D+,D-) on a smooth affine curve. In the present paper we show how to obtain from this description a natural equivariant completion of these \C^*-surfaces. Using elementary transformations we deduce also natural completions for which the boundary divisor is a standard graph in the sense of math.AG/0511063 and show in certain cases their uniqueness. This description is especially precise in the case of normal affine surfaces completable by a zigzag i.e., by a linear chain of smooth rational curves. As an application we classify all zigzags that appear as boundaries of smooth or normal \C^*-surfaces.