  Let $M$ a compact connected orientable 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 K\"ahler surface, for an hermitian metric $h$
sufficiently close to the original K\"ahler metric, the moduli space of
Seiberg-Witten equations relative to the metric $h$ is smooth of the expected
dimension.
