Smooth Affine Surfaces with Non-Unique C*-Actions
| dc.creator | Flenner, Hubert | |
| dc.creator | Kaliman, Shulim | |
| dc.creator | Zaidenberg, Mikhail | |
| dc.date | 2008-09-03 | |
| dc.date | 2008-09-06 | |
| dc.date.accessioned | 2026-07-07T10:00:55Z | |
| dc.date.available | 2026-07-07T10:00:55Z | |
| dc.description | In this paper we complete the classification of effective C*-actions on smooth affine surfaces up to conjugation in the full automorphism group and up to inversion of C*. If a smooth affine surface V admits more than one C*-action then it is known to be Gizatullin i.e., it can be completed by a linear chain of smooth rational curves. In our previous paper we gave a sufficient condition, in terms of the Dolgachev- Pinkham-Demazure (or DPD) presentation, for the uniqueness of a C*-action on a Gizatullin surface. In the present paper we show that this condition is also necessary, at least in the smooth case. In fact, if the uniqueness fails for a smooth Gizatullin surface V which is neither toric nor Danilov-Gizatullin, then V admits a continuous family of pairwise non-conjugated C*-actions depending on one or two parameters. We give an explicit description of all such surfaces and their C*-actions in terms of DPD presentations. We also show that for every k > 0 one can find a Danilov- Gizatullin surface V (n) of index n = n(k) with a family of pairwise non-conjugate C+-actions depending on k parameters. | |
| dc.identifier | https://arxiv.org/abs/0809.0651 | |
| dc.identifier | http://arxiv.org/abs/0809.0651 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168472 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14R05, 14R20, 14J50 | |
| dc.title | Smooth Affine Surfaces with Non-Unique C*-Actions | |
| dc.type | text |