  Let g be a semisimple complex Lie algebra. Let O be a nilpotent orbit in g.
Fix a triangular decomposition g=n+h+n^-. An irreducible component of the
intersection of O and n is called an orbital variety associated to O. It is a
Lagrangian subvariety of O. In this note we discuss the closure of an orbital
variety as a union of varieties. We show that if g contains factors not of type
A_n then there are orbital varieties whose closure contains components which
are not Lagrangian. We show that the argument does not work if all the factors
are of type A_n and provide the facts supporting the conjecture claiming that
if all the factors of g are of type A_n then the closure of an orbital variety
is a union of orbital varieties.
