In mathematics, Luna's slice theorem, introduced by Luna (1973), describes the local behavior of an action of a reductive algebraic group on an affine variety. It is an analogue in algebraic geometry of the theorem that a compact Lie group acting on a smooth manifold X has a slice at each point x, in other words a subvariety W such that X looks locally like G×Gx W. (see slice theorem (differential geometry).)
References
- Luna, Domingo (1973), "Slices étales", Sur les groupes algébriques, Bull. Soc. Math. France, Paris, Mémoire, vol. 33, Paris: Société Mathématique de France, pp. 81–105
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