Soit une variété riemannienne compacte connexe orientée de dimension . On étudie l’espace des structures de classe fondamentale fixée, comme fibré principal de dimension infinie sur la variété des métriques riemanniennes de . 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 de toutes les structures . On montre que, sur une surface de Kähler, pour une métrique hermitienne suffisamment proche à la métrique de Kähler de départ, l’espace de modules de monopôles de Seiberg-Witten relatif à la métrique est lisse de la dimension attendue.
Let a compact connected oriented 4-manifold. We study the space of -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all -structures . We prove that, on a complex Kähler surface, for an hermitian metric sufficiently close to the original Kähler metric, the moduli space of Seiberg-Witten monopoles relative to the metric is smooth of the expected dimension.
@article{AIF_2011__61_3_1259_0,
author = {Scala, Luca},
title = {Perturbations of the metric in Seiberg-Witten equations},
journal = {Annales de l'Institut Fourier},
volume = {61},
year = {2011},
pages = {1259-1297},
doi = {10.5802/aif.2640},
zbl = {1238.57029},
mrnumber = {2918729},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2011__61_3_1259_0}
}
Scala, Luca. Perturbations of the metric in Seiberg-Witten equations. Annales de l'Institut Fourier, Tome 61 (2011) pp. 1259-1297. doi : 10.5802/aif.2640. http://gdmltest.u-ga.fr/item/AIF_2011__61_3_1259_0/
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