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VOL. 1 | 2000 Gauss–Manin Systems of Polynomials of Two Variables can be Made Fuchsian

Abstract

We prove, modulo a conjecture due to A. A. Bolibrukh, that every monodromy group in which the operators of local monodromy in their Jordan normal forms have Jordan blocks of size only $\leq 2$ can be realized by a Fuchsian system of linear differential equations on Riemann's sphere without additional apparent singularities. This implies that the Gauss-Manin system of a polynomial of two variables can always be made Fuchsian if a suitable basis in the cohomologies is chosen.

Information

Published: 1 January 2000
First available in Project Euclid: 5 June 2015

zbMATH: 0979.34066
MathSciNet: MR1758156

Digital Object Identifier: 10.7546/giq-1-2000-105-126

Rights: Copyright © 2000 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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