On the generalized Riemann-Hilbert problem with irregular singularities
经典分析与常微分方程
2007-05-23 v1 代数几何
摘要
We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincare ranks at prescribed singularities, to solve the generalized Riemann-Hilbert problem with irregular singularities. We recover in particular the irreducibility condition on the monodromy given by Bolibrukh and Kostov in the classical case. We apply the above criteria to solve the inverse problem in differential Galois theory with a better control of the singularities.
引用
@article{arxiv.math/0410483,
title = {On the generalized Riemann-Hilbert problem with irregular singularities},
author = {A. A. Bolibruch and S. Malek and C. Mitschi},
journal= {arXiv preprint arXiv:math/0410483},
year = {2007}
}