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Witten triples and the Seiberg–Witten equations on a complex surface
Author(s) -
Dürr Markus
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310226
Subject(s) - mathematics , isomorphism (crystallography) , pure mathematics , equivalence (formal languages) , surface (topology) , class (philosophy) , gauge (firearms) , geometry , crystallography , chemistry , computer science , crystal structure , archaeology , artificial intelligence , history
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)