Let $G$ be a finite group and consider $R=K[V]^G$ be the invariant ring of the group G over the field K of char 0. Let $f\_1,\ldots f\_n$ be a set of primary invariants. Is there a nice geometric characterization of the points where the Jacobian of these polynomials vanishes? For finite reflection groups, this is the reflection hyperplane arrangement...



Jacobian of primary invariants
The points of constant rank of $f=(f\_1,\dots,f\_n)$ essentially are the strata of the stratification into orbit types. See [here](http://www.mat.univie.ac.at/~michor/rep-tens.pdf) or [here](http://www.mat.univie.ac.at/~michor/alg-tens.pdf) and references therein. 


