%0 Journal Article
%T About coordinates on the phase-spaces of Schlesinger system ($n+1$ matrices, $sl(2,C)$-case) and Garnier--Painlev¨¦ 6 system
%A Mikhail V. Babich
%J Mathematics
%D 2006
%I arXiv
%X 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 ${sl(2,\mathbb C)}$ is constructed. The explicit polynomial map of the Cartesian products of $n-2$ 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.
%U http://arxiv.org/abs/math/0605544v1