Completions of $\C^*$-surfaces
| dc.creator | Flenner, Hubert | |
| dc.creator | Kaliman, Shulim | |
| dc.creator | Zaidenberg, Mikhail | |
| dc.date | 2005-11-10 | |
| dc.date.accessioned | 2026-07-07T06:51:07Z | |
| dc.date.available | 2026-07-07T06:51:07Z | |
| dc.description | 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. | |
| dc.description | 37 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511282 | |
| dc.identifier | http://arxiv.org/abs/math/0511282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104881 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14R05, 14R20, 14J50 | |
| dc.title | Completions of $\C^*$-surfaces | |
| dc.type | text |