About coordinates on the phase-spaces of Schlesinger system ($n+1$ matrices, $sl(2,C)$-case) and Garnier--Painlev\'e 6 system
Symplectic Geometry
2007-05-23 v1 Classical Analysis and ODEs
Abstract
The geometric model of the pathway linking Schlesinger and Garnier--Painlev\'e~6 systems based on an original orthonormalization of a set of elements in is constructed. The explicit polynomial map of the Cartesian products of quadrics (the Zariski-topology chart of the phase space of the Garnier--Painlev\'e~6 system) into the phase space of the Schlesinger system and the rational inverse to this map are presented.
Keywords
Cite
@article{arxiv.math/0605544,
title = {About coordinates on the phase-spaces of Schlesinger system ($n+1$ matrices, $sl(2,C)$-case) and Garnier--Painlev\'e 6 system},
author = {Mikhail V. Babich},
journal= {arXiv preprint arXiv:math/0605544},
year = {2007}
}