Invariant Rings and Quasiaffine Quotients
| dc.creator | Winkelmann, Joerg | |
| dc.date | 2000-07-12 | |
| dc.date.accessioned | 2026-07-07T04:36:21Z | |
| dc.date.available | 2026-07-07T04:36:21Z | |
| dc.description | We study Hilbert's fourteenth problem from a geometric point of view. Nagata's celebrated counterexample demonstrates that for an arbitrary group action on a variety the ring of invariant functions need not be isomorphic to the ring of functions of an affine variety. Nevertheless one can prove that such a ring of invariants is always isomorphic to the ring of functions on a quasi-affine variety. Conversely, for a given quasi-affine variety V there exists always an action of the additive group on some affine variety W such that the ring of functions of V is isomorphic to the ring of invariant functions on W. Thus a k-algebra occurs as invariant ring for some group acting on a k-variety iff it occurs as function ring for some quasi-affine k-variety. | |
| dc.description | 11 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0007076 | |
| dc.identifier | http://arxiv.org/abs/math/0007076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59564 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A50, 14R20, 14L30 | |
| dc.title | Invariant Rings and Quasiaffine Quotients | |
| dc.type | text |