Universal isomonodromic deformations of meromorphic rank 2 connections on curves

Viktoria Heu (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby more elementary than the construction in arbitrary rank due to B. Malgrange and I. Krichever and it includes the case of resonant singularities in a natural way.

Mots clés: déformations isomonodromiques; connexions méromorphes

Domaines: Variables complexes [math.CV]

Viktoria Heu. Universal isomonodromic deformations of meromorphic rank 2 connections on curves. Annales de l'Institut Fourier, 2010, 60 (2), pp.515-549. ⟨hal-00377019⟩