Geodesic
The~Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 370-386

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce a way to represent pairs $(E,\nabla)$, where $E$ is a bundle on a Riemann surface and $\nabla$ is a logarithmic connection in $E$, based on a representation of the surface as the quotient of the exterior of the unit disc. In this representation, we write the local isomonodromic deformation conditions for the pairs $(E,\nabla)$. These conditions are written as a modified Schlesinger system on a Riemann sphere (reduced to the ordinary Schlesinger system in the typical case) supplemented by a certain system of linear equations.
Mots-clés : isomonodromic deformation
Keywords: Riemann surface, Schlesinger system. 
@article{TMF_2012_171_3_a1,
     author = {D. V. Artamonov},
     title = {The~Schlesinger system and isomonodromic deformations of bundles with connections on {Riemann} surfaces},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {370--386},
     publisher = {mathdoc},
     volume = {171},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a1/}
}
TY  - JOUR
AU  - D. V. Artamonov
TI  - The~Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 370
EP  - 386
VL  - 171
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a1/
LA  - ru
ID  - TMF_2012_171_3_a1
ER  - 
%0 Journal Article
%A D. V. Artamonov
%T The~Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 370-386
%V 171
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a1/
%G ru
%F TMF_2012_171_3_a1
D. V. Artamonov. The~Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 370-386. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a1/