  Let G be a semisimple group over an algebraically closed field. Steinberg has
associated to a Coxeter element w of minimal length r a subvariety V of G
isomorphic to an affine space of dimension r which meets the regular unipotent
class Y in exactly one point. In this paper this is generalized to the case
where w is replaced by any elliptic element in the Weyl group of minimal length
d in its conjugacy class, V is replaced by a subvariety V' of G isomorphic to
an affine space of dimension d and Y is replaced by a unipotent class Y' of
codimension d in such a way that the intersection of V' and Y' is finite.
