Let X be a closed, oriented, smooth 4-manifold. For every element v of H1(X;Z/2) one can associate a bundle L of infinite cyclic groups over X (or more precisely: an isomorphism class of such bundles). Using singular (co)homology with coefficients in this bundle one can define in the usual way an "intersection form" Q_v on H_2(X;L) / torsion, and this form is unimodular. In the 1980's Donaldson proved, using instanton moduli spaces, that if the usual intersection form Q_0 is definite then it must be diagonal. Until recently, little seemed to be known about Q_v when v is non-zero. In this talk I will show that there are in fact constraints on the definite Q_v. The proof introduces some new twists to the ideas of Donaldson.