AbstractSuppose G is a connected reductive algebraic group,Pis a parabolic subgroup of G,Lis a Levi factor ofP, and e is a regular nilpotent element in Lie L. We assume that the characteristic of the underlying field is good for G. Choose a maximal torus,T, and a Borel subgroup,B, of G, so that T⊆B∩L,B ⊆ Pande ∈LieB.Let β be the variety of Borel subgroups ofGand let