Luna's slice theorem

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×_{G_x} W. (see slice theorem (differential geometry).)

References

Luna, Domingo (1973), "Slices étales", Sur les groupes algébriques, Bull. Soc. Math. France, Paris, Mémoire 33, Paris: Société Mathématique de France, pp. 81–105