  The real intersection cohomology of a toric variety is described in a purely
combinatorial way using methods of elementary commutative algebra only. We
define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the
fan as an axiomatic characterization of the equivariant intersection cohomology
sheaf. This provides a purely algebraic interpretation of Stanley's generalized
f- and g-vector of an arbitrary polytope or complete fan under a natural
vanishing condition. -- The results presented in this note originate from joint
work with G.Barthel, J.-P.Brasselet and L.Kaup, continuing earlier research
(see math.AG/9904159). A detailed exposition will appear elsewhere (see
math.AG/0002181).
