Singularities of the moduli space of Yang-Mills fields
type: Item
instance of: scholarly article
title: Singularities of the moduli space of Yang-Mills fields
zbMATH Open document ID: 0629.32020
author: Mitsuhiro Itoh
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: The moduli space of anti self-dual instantons on a \({\mathfrak G}\)-bundle (\({\mathfrak G}\) compact, semisimple) over a Kähler surface is a complex manifold with possible singularities. This note considers the structure of the singularities which can occur. They are shown to fall into (possibly mixtures of) two types. The first occur at reducible instantons where the isotropy subgroup of the gauge group action `jumps'. Around the second type the moduli space looks like the zero point set of an analytic function. The case of a compact surface is also considered and here there are no singularities purely of the first type. Lastly for \({\mathfrak G}={\mathfrak SU}(2)\) the structure of the reducible connections is investigated.
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 32Sxx
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4023699
zbMATH Keywords: Yang-Mills
zbMATH Keywords: moduli space of anti self-dual instantons
zbMATH Keywords: Kähler surface
zbMATH Keywords: singularities
reviewed by: Michael K. Murray
MaRDI profile type: Publication
full work available at URL: pjaa.63.170
OpenAlex ID: W2062758329
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DOI: 10.3792/PJAA.63.170
description: scientific article; zbMATH DE number 4023699