A Hilbert-Mumford criterion for SL_2-actions
| dc.creator | Hausen, Juergen | |
| dc.date | 2002-11-26 | |
| dc.date.accessioned | 2026-07-07T04:53:19Z | |
| dc.date.available | 2026-07-07T04:53:19Z | |
| dc.description | Let the special linear group $G := SL_{2}$ act regularly on a $Q$-factorial variety $X$. Consider a maximal torus $T \subset G$ and its normalizer $N \subset G$. We prove: If $U \subset X$ is a maximal open $N$-invariant subset admitting a good quotient $U \to U // N$ with a divisorial quotient space, then the intersection $W(U)$ of all translates $g \dot U$ is open in $X$ and admits a good quotient $W(U) \to W(U) // G$ with a divisorial quotient space. Conversely, we obtain that every maximal open $G$-invariant subset $W \subset X$ admitting a good quotient $W \to W // G$ with a divisorial quotient space is of the form $W = W(U)$ for some maximal open $N$-invariant $U$ as above. | |
| dc.description | 9 pages, to appear in Coll. Math | |
| dc.identifier | https://arxiv.org/abs/math/0211412 | |
| dc.identifier | http://arxiv.org/abs/math/0211412 | |
| dc.identifier | Coll. Math. Vol. 97, No. 2, 151-161 (2003) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65799 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L24, 14L30 | |
| dc.title | A Hilbert-Mumford criterion for SL_2-actions | |
| dc.type | text |