Perturbations of the metric in Seiberg-Witten equations

2009/02/26 by Luca Scala, Scala, Luca
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0902.4690

openalex publication_date 2009/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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