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arXiv · 1104.4184

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

D. V. Artamonov
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Abstract

We introduce a way of presentation of pairs $(E,\nabla)$, where $E$ is a bundle on a Riemann surface and $\nabla$ is a logarithmic connection in $E$, which is based on a presentation of the surface as a factor of the exterior of the unit disc. In this presentation we write the local equation of isomonodormic deformation of pairs $(E,\nabla)$. These conditions are written as a modified Schlesinger system on a Riemann sphere (and in the typical case just as an ordinary Schlesinger system) plus some linear system.

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BibTeXRIS

D. V. Artamonov. 2011-04-21. The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces. https://doi.org/10.1007/s11232-012-0071-0

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