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

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• 作者：Jaeyoo Choy ^{choy@knu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：14D21 ; 81T13
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：106
• 期：Complete
• 页码：284-304
• 全文大小：565 K

文摘

Let 549615b01360869815f31bc52f74fdd" title="Click to view the MathML source">K$K$ be the compact Lie group $\mathrm{USp}(N/2)$ or $\mathrm{SO}(N,\mathbb{R})$. Let ${\mathcal{M}}_n^K$ be the moduli space of framed 549615b01360869815f31bc52f74fdd" title="Click to view the MathML source">K$K$-instantons over 5498697a9425960f8e565d4737bf78ee" title="Click to view the MathML source">S⁴$S^4$ with the instanton number n$n$. By Donaldson (1984), ${\mathcal{M}}_n^K$ is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ⁻¹(0)$\mu {}^{-1}\left(0\right)$, where 4e14424bc4030a9410" title="Click to view the MathML source">μ$\mu$ is a holomorphic moment map such that μ⁻¹(0)$\mu {}^{-1}\left(0\right)$ consists of the ADHM data.

The purpose of the paper is to study the geometric properties of μ⁻¹(0)$\mu {}^{-1}\left(0\right)$ and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If e171d74ee1c7f0b28f7b696500">$K=\mathrm{USp}(N/2)$ then 4e14424bc4030a9410" title="Click to view the MathML source">μ$\mu$ is flat and μ⁻¹(0)$\mu {}^{-1}\left(0\right)$ is an irreducible normal variety for any n$n$ and even N$N$. If $K=\mathrm{SO}(N,\mathbb{R})$ the similar results are proven for low n$n$ and N$N$.

As an application one can obtain a mathematical interpretation of the 549615b01360869815f31bc52f74fdd" title="Click to view the MathML source">K$K$-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).