Modular forms and Donaldson invariants for 4manifolds with $b_+=1$
Abstract
We study the Donaldson invariants of simply connected $4$manifolds with $b_+=1$, and in particular the change of the invariants under wallcrossing. We assume the conjecture of Kotschick and Morgan about the shape of the wallcrossing terms (which Oszvath and Morgan are now able to prove), and are determine a generating function for the wallcrossing 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.
 Publication:

arXiv eprints
 Pub Date:
 June 1995
 arXiv:
 arXiv:alggeom/9506018
 Bibcode:
 1995alg.geom..6018G
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 I correct a number of missing attributions and citations. In particular this applies to the cited paper of Kotschick and Lisca "Instanton invariants via topology", which contains some ideas which have been important for this work. AMSLaTeX