Perturbations of the metric in Seiberg-Witten equations
Annales de l'Institut Fourier, Volume 61 (2011) no. 3, pp. 1259-1297.

Let M a compact connected oriented 4-manifold. We study the space Ξ of Spin c -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on M. In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all Spin c -structures Ξ. We prove that, on a complex Kähler surface, for an hermitian metric h sufficiently close to the original Kähler metric, the moduli space of Seiberg-Witten monopoles relative to the metric h is smooth of the expected dimension.

Soit M une variété riemannienne compacte connexe orientée de dimension 4. On étudie l’espace Ξ des structures Spin c de classe fondamentale fixée, comme fibré principal de dimension infinie sur la variété des métriques riemanniennes de M. Afin d’étudier les perturbations de la métrique dans les équations de Seiberg-Witten, on étudie la transversalité des équations universelles, paramétrées par l’espace Ξ de toutes les structures Spin c . On montre que, sur une surface de Kähler, pour une métrique hermitienne h suffisamment proche à la métrique de Kähler de départ, l’espace de modules de monopôles de Seiberg-Witten relatif à la métrique h est lisse de la dimension attendue.

DOI: 10.5802/aif.2640
Classification: 57R57,  58G03,  58D27,  14J80
Keywords: Seiberg-Witten theory, perturbations of the metric, Kähler surfaces, transversality
Scala, Luca 1

1 University of Chicago Department of Mathematics 5734 S. University Avenue 60637 Chicago IL (USA)
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Scala, Luca. Perturbations of the metric in Seiberg-Witten equations. Annales de l'Institut Fourier, Volume 61 (2011) no. 3, pp. 1259-1297. doi : 10.5802/aif.2640. http://archive.numdam.org/articles/10.5802/aif.2640/

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