Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 51, Number 2 (2011), 263-335.
Perverse coherent sheaves on blowup, III: Blow-up formula from wall-crossing
In earlier papers of this series we constructed a sequence of intermediate moduli spaces connecting a moduli space of stable torsion-free sheaves on a nonsingular complex projective surface and 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 to and then from to . 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 supersymmetric gauge theory, found and used to derive the Seiberg-Witten curves.
Kyoto J. Math., Volume 51, Number 2 (2011), 263-335.
First available in Project Euclid: 22 April 2011
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. https://projecteuclid.org/euclid.kjm/1303494505