PERTURBATIONS OF THE METRIC IN SEIBERG-WITTEN EQUATIONS

Let M a compact connected oriented 4-manifold. We study the space Xi 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 Xi. We prove that, on a complex Kahler surface, for an hermitian metric h sufficiently close to the original Kahler metric, the moduli space of Seiberg-Witten monopoles relative to the metric h is smooth of the expected dimension.