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.
Keywords: Isomonodromic deformation, meromorphic connection
Mot clés : déformation isomonodromique, connexion méromorphe
@article{AIF_2010__60_2_515_0, author = {Heu, Viktoria}, title = {Universal isomonodromic deformations of meromorphic rank 2 connections on curves}, journal = {Annales de l'Institut Fourier}, pages = {515--549}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {2}, year = {2010}, doi = {10.5802/aif.2531}, zbl = {1193.32009}, mrnumber = {2667785}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2531/} }
TY - JOUR AU - Heu, Viktoria TI - Universal isomonodromic deformations of meromorphic rank 2 connections on curves JO - Annales de l'Institut Fourier PY - 2010 SP - 515 EP - 549 VL - 60 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2531/ DO - 10.5802/aif.2531 LA - en ID - AIF_2010__60_2_515_0 ER -
%0 Journal Article %A Heu, Viktoria %T Universal isomonodromic deformations of meromorphic rank 2 connections on curves %J Annales de l'Institut Fourier %D 2010 %P 515-549 %V 60 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2531/ %R 10.5802/aif.2531 %G en %F AIF_2010__60_2_515_0
Heu, Viktoria. Universal isomonodromic deformations of meromorphic rank 2 connections on curves. Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 515-549. doi : 10.5802/aif.2531. http://www.numdam.org/articles/10.5802/aif.2531/
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