  We study the Donaldson invariants of simply connected $4$-manifolds with
$b_+=1$, and in particular the change of the invariants under wall-crossing. We
assume the conjecture of Kotschick and Morgan about the shape of the
wall-crossing terms (which Oszva\'th and Morgan are now able to prove), and are
determine a generating function for the wall-crossing terms in terms of modular
forms. As an application we determine all the Donaldson invariants of the
projective plane in terms of modular forms. The main tool are the blowup
formulas, which are used to obtain recursive relations.
