### Perturbations of the metric in Seiberg-Witten equations

Let $M$ a compact connected oriented 4-manifold. We study the space $\Xi $ of ${\mathrm{Spin}}^{\mathrm{c}}$-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 ${\mathrm{Spin}}^{\mathrm{c}}$-structures $\Xi $. We prove that, on a complex Kähler surface, for an hermitian metric $h$ sufficiently close to the original Kähler metric, the moduli space...