  Let G be a complex reductive group and V a G-module. Let \pi: V \to V//G be
the quotient morphism and set N(V) = \pi^{-1}(\pi(0)). We consider the
following question. Is the null cone N(V) reduced, i.e., is the ideal of N(V)
generated by G-invariant polynomials? We have complete results when G is SL_2,
SL_3 or a simple group of adjoint type, and also when G is semisimple of
adjoint type and the G-module V is irreducible.
