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TMF, 2012, Volume 171, Number 3, Pages 370–386 (Mi tmf6899)  

The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces

D. V. Artamonov

M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: 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.

Keywords: isomonodromic deformation, Riemann surface, Schlesinger system

DOI: https://doi.org/10.4213/tmf6899

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English version:
Theoretical and Mathematical Physics, 2012, 171:3, 739–753

Bibliographic databases:

Received: 20.04.2011
Revised: 18.08.2011

Citation: D. V. Artamonov, “The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces”, TMF, 171:3 (2012), 370–386; Theoret. and Math. Phys., 171:3 (2012), 739–753

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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