  Inside a product of projective spaces, we try to understand which Chow
classes come from irreducible subvarieties. The answer is closely related to
the theory of integer polymatroids. The support of a representable class can be
(partially) characterized as some integer point inside a particular
polymatroid. If the class is multiplicity-free, we obtain a complete
characterization in terms of representable polymatroids. We also generalize
some of the results to the case of products of Grassmannians.
