Instanton counting, Donaldson invariants and line bundles on
moduli spaces of sheaves on 
rational surfaces
 -- Lothar Göttsche

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This is joint work with Nakajima and Yoshioka.
For a rational algebraic surface we express the Donaldson
invariants in terms of the Nekrasov partition function
(which could be viewed as generating function of "Donaldson
invariants of the affine plane").

<p>

In a very similar manner we express the holomorphic Euler
characteristics of line bundles on the moduli spaces of stable
rank 2 sheaves on rational surfaces  in terms of the
K-theoretic Nekrasov partition function.

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In both cases the method of proof is to study the behaviour of the
formula under wallcrossing via localization.