Inventiones mathematicae

, Volume 162, Issue 2, pp 313–355

Instanton counting on blowup. I. 4-dimensional pure gauge theory


    • Department of MathematicsKyoto University
    • Department of Mathematics, Faculty of ScienceKobe University

DOI: 10.1007/s00222-005-0444-1

Cite this article as:
Nakajima, H. & Yoshioka, K. Invent. math. (2005) 162: 313. doi:10.1007/s00222-005-0444-1


We give a mathematically rigorous proof of Nekrasov’s conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on ℝ4 gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of ℝ4, we derive a differential equation for the Nekrasov’s partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al.

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© Springer-Verlag 2005