ar X iv : m at h / 05 11 30 0 v 1 [ m at h . A G ] 1 1 N ov 2 00 5 Typical separating invariants

It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the G–modules W and m copies of V can be separated by polynomial invariants, then they can be separated by invariants depending only on ≤ 2 dim(V ) variables of type V ; when G is reductive, invariants depending only on ≤ dim(V ) + 1 variables suffice. Similar result is valid for rational invariants. Explicit bounds on the number of type V variables in a typical system of separating invariants are given for the binary polyhedral groups, and this is applied to the invariant theory of binary forms.