Group actions, $k$-derivations and finite morphisms

dc.creatorBonnet, Philippe
dc.date2006-04-06
dc.date.accessioned2026-07-07T07:10:37Z
dc.date.available2026-07-07T07:10:37Z
dc.descriptionLet $G$ 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.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0604148
dc.identifierhttp://arxiv.org/abs/math/0604148
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111474
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14L24; 13N15
dc.titleGroup actions, $k$-derivations and finite morphisms
dc.typetext

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