Torsors over Luna strata

Abstract

Let G be a reductive group and X H be a Luna stratum on the quotient space V //G of a rational G-module V . We consider torsors over X H with both non-commutative and commutative structure groups. It allows us to describe the divisor class group and the Cox ring of a Luna stratum under mild assumptions. This approach gives a simple cause why many Luna strata are singular along their boundary.

On orbits of the automorphism group on an affine toric variety

“…In particular, in our settings the Luna stratification is intrinsic in the sense of [13]. For connections between quotient presentations of an arbitrary affine variety, the Luna stratification, and Cox rings, see [1].…”