  Let g be a semisimple Lie algebra of finite dimension. The nullcone N of g is
the set of (x,y) in g x g such that x and y are nilpotents and are in the same
Borel sualgebra. The main result of this paper is that N is a closed and
irreducible subvariety of g x g, its normalisation has rational singularities
and its normalization morphism is bijective.
