2006/04/06 by Philippe Bonnet, Bonnet, Philippe
Mathematics · #13N15 #14L24 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AG #msc:13N15 #msc:14L24
paper · pdf · doi:10.48550/arxiv.math/0604148
10 pages
arxiv created 2006/04/06 · openalex publication_date 2006/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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→ Y of irreducible affine G-varieties. First we determine under which conditions on Y the induced map FG:X//G→ Y//G of quotient varieties is also finite. This result is reformulated in terms of kernels of derivations on k-algebras A⊂ B such that B is integral over A. Second we construct explicitly two examples of finite G-equivariant maps F. In the first one, FG is quasifinite but not finite. In the second one, FG is not even quasifinite.