Isomonodromic deformations and maximally stable bundles

Viktoria Heu (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider irreducible tracefree meromorphic rank 2 connections over compact Riemann surfaces. By deforming the curve, the position of the poles and the connection, we construct the universal isomonodromic deformation of such a connection. We prove that the underlying vector bundle is generically maximally stable along the deformation. For surfaces of genus greater than 1, we get a non-trivial result even for regular connections.

Keywords: meromorphic connections; isomonodromic deformations; Riemann-Hilbert correspondence; stable vector bundles

Domains: Complex Variables [math.CV]; Differential Geometry [math.DG]

Viktoria Heu. Isomonodromic deformations and maximally stable bundles. 2008. ⟨hal-00308586v2⟩