  Given a graph G (or more generally a matroid embedded in a projective space),
we construct a sequence of varieties whose geometry encodes combinatorial
information about G. For example, the chromatic polynomial of G (giving at each
m>0 the number of colorings of G with m colors, such that no adjacent vertices
are assigned the same color) can be computed as an intersection product between
certain classes on these varieties, and other information such as Crapo's
invariant find a very natural geometric counterpart. The note presents this
construction, and gives `geometric' proofs of a number of standard
combinatorial results on the chromatic polynomial.
