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The coupled Seiberg-Witten equations, vortices, and moduli spaces of stable pairs


Okonek, C; Teleman, A (1995). The coupled Seiberg-Witten equations, vortices, and moduli spaces of stable pairs. International Journal of Mathematics, 6(6):893-910.

Abstract

We introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a moduli space of holomorphic stable pairs. In the rank 1 case, one recovers Witten's result identifying the space of irreducible monopoles with a moduli space of divisors. As application, we give a short proof of the fact that a rational surface cannot be diffeomorphic to a minimal surface of general type.

Abstract

We introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a moduli space of holomorphic stable pairs. In the rank 1 case, one recovers Witten's result identifying the space of irreducible monopoles with a moduli space of divisors. As application, we give a short proof of the fact that a rational surface cannot be diffeomorphic to a minimal surface of general type.

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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
Language:English
Date:1995
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:27
Publisher:World Scientific Publishing
ISSN:0129-167X
Additional Information:Electronic version of an article published as [Internat. J. Math. 6 (1995), no. 6] http://dx.doi.org/10.1142/S0129167X95000390 © 1995 copyright World Scientific Publishing Company http://www.worldscinet.com/ijm/ijm.shtml
Publisher DOI:https://doi.org/10.1142/S0129167X95000390
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0846.57013
http://www.ams.org/mathscinet-getitem?mr=1354000

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