Kyoto Journal of Mathematics

Perverse coherent sheaves on blowup, III: Blow-up formula from wall-crossing

Hiraku Nakajima and Kōta Yoshioka

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In earlier papers of this series we constructed a sequence of intermediate moduli spaces {m(c)}m=0,1,2, connecting a moduli space M(c) of stable torsion-free sheaves on a nonsingular complex projective surface X and (c) on its one-point blow-up . They are moduli spaces of perverse coherent sheaves on . In this paper we study how Donaldson-type invariants (integrals of cohomology classes given by universal sheaves) change from m(c) to m+1(c) and then from M(c) to (c). As an application we prove that Nekrasov-type partition functions satisfy certain equations that determine invariants recursively in second Chern classes. They are generalizations of the blow-up equation for the original Nekrasov deformed partition function for the pure N=2 supersymmetric gauge theory, found and used to derive the Seiberg-Witten curves.

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Kyoto J. Math., Volume 51, Number 2 (2011), 263-335.

First available in Project Euclid: 22 April 2011

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Primary: 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]
Secondary: 16G20: Representations of quivers and partially ordered sets


Nakajima, Hiraku; Yoshioka, Kōta. Perverse coherent sheaves on blowup, III: Blow-up formula from wall-crossing. Kyoto J. Math. 51 (2011), no. 2, 263--335. doi:10.1215/21562261-1214366.

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