Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions
| Autor: | Choy, Jaeyoo |
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| Rok vydání: | 2016 |
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| Zdroj: | J. Geom. Phys. 106 (2016) 284--304; 110 (2016), 343--347 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.geomphys.2016.04.011 |
| Popis: | Let $K$ be the compact Lie group $USp(N/2)$ or $SO(N, R)$. Let $M^K_n$ be the moduli space of framed K-instantons over $S^4$ with the instanton number $n$. By Donaldson (1984), $M^K_n$ 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). Comment: 32 pages, 1 figure; 7 pages (corrigendum and addendum) |
| Databáze: | arXiv |
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