Slodowy, Peter [Knop, Friedrich] The slice theorem for algebraic transformation groups. – Appendix: Proof of the fundamental lemma and of the slice theorem (by Friedrich Knop). (Der Scheibensatz für algebraische Transformationsgruppen. – Anhang: Beweis des Fundamentallemmas und des Scheibensatzes (von Friedrich Knop).) (German) Zbl 0722.14031 Algebraische Transformationsgruppen und Invariantentheorie, DMV Semin. 13, 89-113; Anhang: 110-113 (1989). [For the entire collection see Zbl 0682.00008.] The topic of this lecture is a discussion of Luna’s slice theorem [D. Luna, Bull. Soc. Math. Fr., Suppl., Mém. 33, 81-105 (1973; Zbl 0286.14014)]. The slice theorem treats the local structure of the action of a reductive algebraic group on an affine variety. The goal is to reduce this structure to get information about the action of the stabilizator on a suitable slice at the orbit of a point. The author formulates the theorem by some preliminaries and gives some applications. - The slice theorem is useful for the study of singularities and for the orbit classification. As an appendix the reader finds a simplified version of Luna’s unpublished proof given by F. Knop. Reviewer: K.Drechsler (Halle-Neustadt) Cited in 9 Documents MSC: 14L30 Group actions on varieties or schemes (quotients) 14B05 Singularities in algebraic geometry 57S25 Groups acting on specific manifolds 14M17 Homogeneous spaces and generalizations Keywords:quotient variety; slice theorem; action of a reductive algebraic group; singularities; orbit classification Citations:Zbl 0682.00008; Zbl 0286.14014 PDFBibTeX XML