Group actions, $k$-derivations and finite morphisms
| dc.creator | Bonnet, Philippe | |
| dc.date | 2006-04-06 | |
| dc.date.accessioned | 2026-07-07T07:10:37Z | |
| dc.date.available | 2026-07-07T07:10:37Z | |
| dc.description | Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which conditions on $Y$ the induced map $F^G:X//G\to Y//G$ of quotient varieties is also finite. This result is reformulated in terms of kernels of derivations on $k$-algebras $A\subset B$ such that $B$ is integral over $A$. Second we construct explicitly two examples of finite $G$-equivariant maps $F$. In the first one, $F^G$ is quasifinite but not finite. In the second one, $F^G$ is not even quasifinite. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604148 | |
| dc.identifier | http://arxiv.org/abs/math/0604148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111474 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14L24; 13N15 | |
| dc.title | Group actions, $k$-derivations and finite morphisms | |
| dc.type | text |