Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions

JOURNAL OF GEOMETRY AND PHYSICS

卷:106

Article

Choy, Jaeyoo¹ 

[1] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

关键词: Moduli spaces;    Framed symplectic and orthogonal bundles;    Instantons;    K-theoretic Nekrasov partition functions;   

DOI  :  10.1016/j.geomphys.2016.04.011

来源: Elsevier

【 摘 要 】

Let K be the compact Lie group USp(N/2) or SO(N, R). Let M-n(K) be the moduli space of framed K-instantons over S-4 with the instanton number n. By Donaldson (1984), M-n(K) is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of mu(-1)(0), where mu is a holomorphic moment map such that mu(-1)(0) consists of the ADHM data. The purpose of the paper is to study the, geometric properties of mu(-1)(0) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K = USp(N/2) then mu is flat and mu(-1)(0) is an irreducible normal variety for any n and even N. If K = SO(N, R) the similar results are proven for low n and N. As an application one can obtain a mathematical interpretation of the K-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004). (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free