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Summer 2011 Perverse coherent sheaves on blowup, III: Blow-up formula from wall-crossing
Hiraku Nakajima, Kōta Yoshioka
Kyoto J. Math. 51(2): 263-335 (Summer 2011). DOI: 10.1215/21562261-1214366


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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Hiraku Nakajima. Kōta Yoshioka. "Perverse coherent sheaves on blowup, III: Blow-up formula from wall-crossing." Kyoto J. Math. 51 (2) 263 - 335, Summer 2011.


Published: Summer 2011
First available in Project Euclid: 22 April 2011

zbMATH: 1220.14012
MathSciNet: MR2793270
Digital Object Identifier: 10.1215/21562261-1214366

Primary: 14D21
Secondary: 16G20

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 2 • Summer 2011
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