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Witten triples and the Seiberg-Witten equations on a complex surface


Dürr, M (2005). Witten triples and the Seiberg-Witten equations on a complex surface. Mathematische Nachrichten, 278(1-2):53-76.

Abstract

We study the solutions of the Seiberg-Witten equations on complex surfaces. We show that for a large class of parameters, the gauge equivalence classes of irreducible solutions of the twisted Seiberg-Witten equations correspond to stable Witten triples. We prove that on Kähler surfaces this correspondence is the set-theoretical support of an isomorphism of real-analytic spaces. This makes it possible to take multiplicities into account and generalizes and unifies results previously obtained by Witten. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the solutions of the Seiberg-Witten equations on complex surfaces. We show that for a large class of parameters, the gauge equivalence classes of irreducible solutions of the twisted Seiberg-Witten equations correspond to stable Witten triples. We prove that on Kähler surfaces this correspondence is the set-theoretical support of an isomorphism of real-analytic spaces. This makes it possible to take multiplicities into account and generalizes and unifies results previously obtained by Witten. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Complex surfaces • Seiberg-Witten equations • Kobayashi-Hitchin correspondence
Language:English
Date:2005
Deposited On:19 Feb 2010 15:32
Last Modified:05 Apr 2016 13:24
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0025-584X
Publisher DOI:https://doi.org/10.1002/mana.200310226

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