  We observe a general structure theorem for quantum cohomology rings, a
non-homogeneous version of the usual cohomology ring encoding information about
(almost holomorphic) rational curves. An application is the rigorous
computation of the quantum cohomology of Grassmannians. As purely algebraic
consequence we prove a beautiful formula of Vafa and Intriligator for
intersection numbers of certain compactifications of moduli spaces of maps from
a Riemann surface (any genus) to G(k,n) which recently has excited many
mathematicians. The formula generalizes to any Fano manifold whose cohomology
ring can be presented as complete intersection.
