Instanton counting and Donaldson invariants
Abstract
For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture math.AG/0306198, hep-th/0306238, math.AG/0409441 and its refinement math.AG/0311058, we apply this result to give a generating function for the wallcrossing of Donaldson invariants of good walls of simply connected projective surfaces with in terms of modular forms. This formula was proved earlier in alg-geom/9506018 more generally for simply connected 4-manifolds with , assuming the Kotschick-Morgan conjecture and it was also derived by physical arguments in hep-th/9709193.
Keywords
Cite
@article{arxiv.math/0606180,
title = {Instanton counting and Donaldson invariants},
author = {Lothar Göttsche and Hiraku Nakajima and Kota Yoshioka},
journal= {arXiv preprint arXiv:math/0606180},
year = {2007}
}
Comments
45pages, typos corrected, update the reference to a new version of Mochizuki's paper math.AG/0210211