Vector fields and Luna strata. (Q1946080)

Let \(G\) be a complex reductive group, and let \(V\) be a \(G\)-module with invariant-theoretic quotient variety \(Z\). This \(Z\) has a finite stratification by isotropy type called the Luna stratification. The author shows that in many cases this stratification is intrinsic, i.e, preserved under every automorphism of \(Z\). The key is to consider the vector fields on \(Z\).