Universal isomonodromic deformations of meromorphic rank 2 connections on curves

Heu, Viktoria

Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 515-549.

Nous considérons les fibrés à connexion méromorphe sans trace de rang 2 sur les surfaces de Riemann compactes de genre quelconque. En déformant la courbe, la position des pôles et le fibré à connexion, nous construisons la déformation isomonodromique universelle globale d’un tel fibré à connexion initial. Notre construction spécifique au cas du rang 2 et sans trace est plus élémentaire que la construction en rang quelconque due à B. Malgrange et I. Krichever au sens où elle ne nécessite pas d’analyse de Stokes des singularités irrégulières. De plus, elle englobe le cas des singularités résonantes de manière naturelle.

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.

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