Geometry of Higgs and Toda fields on Riemann surfaces
type: Item
instance of: scholarly article
title: Geometry of Higgs and Toda fields on Riemann surfaces
zbMATH Open document ID: 0841.14005
DOI: 10.1016/0393-0440(94)00038-6
author: E. Aldrovandi
author: G. Falqui
published in: Journal of Geometry and Physics
publication date: 1996-07-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/9312093
review text: Für Riemannsche Flächen vom Geschlecht \(> 1\) wird eine Beziehung zwischen Toda-Gleichungen und Higgs-Systemen hergestellt: Jede Lösung von Toda-Gleichungen definiert eine Lösung einer Hitchin-Gleichung eines bestimmten Higgs-Bündels. Eine weitere Querverbindung zwischen beiden wird durch \(W_n\)-Algebren geliefert. Eine sehr interessante Konsequenz ergibt sich durch eine Interpretation des Toda-Zusammenhangs durch Variation von Hodge-Strukturen: Die Riemannsche Fläche läßt sich holomorph in den Quotienten des Griffithschen Periodengebiets nach der Monodromiegruppe einbetten.
Mathematics Subject Classification ID: 14D07
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 14H55
zbMATH DE Number: 806358
zbMATH Keywords: Toda equation
zbMATH Keywords: Higgs system
zbMATH Keywords: variation of Hodge structure
zbMATH Keywords: Riemann surface
reviewed by: Jürgen Wolfart
MaRDI profile type: Publication
OpenAlex ID: W2092072870
arXiv ID: hep-th/9312093
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description: scientific article