Perturbations of the metric in Seiberg-Witten equations (Q660446)

The paper deals with perturbations of the metric in the Seiberg-Witten equations. The author studies the space \(\Xi\) of \(Spin^c\)-structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of Riemannian metrics on a compact connected oriented \(4\)-manifold \(M\). The author shows that, on a complex Kähler surface, for a 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.