# Moduli of Stable Parabolic Connections, Riemann-Hilbert Correspondence and Geometry of Painlev\'{e} Equation of Type VI, Part II

@article{Inaba2003ModuliOS,
title={Moduli of Stable Parabolic Connections, Riemann-Hilbert Correspondence and Geometry of Painlev\'\{e\} Equation of Type VI, Part II},
author={Michi-aki Inaba and Katsunori Iwasaki and Masahiko Saito},
journal={arXiv: Algebraic Geometry},
year={2003}
}
• Published 20 September 2003
• Mathematics
• arXiv: Algebraic Geometry
In this paper, we show that the family of moduli spaces of $\balpha'$-stable $(\bt, \blambda)$-parabolic $\phi$-connections of rank 2 over $\BP^1$ with 4-regular singular points and the fixed determinant bundle of degree -1 is isomorphic to the family of Okamoto--Painlev\'e pairs introduced by Okamoto \cite{O1} and \cite{STT02}. We also discuss about the generalization of our theory to the case where the rank of the connections and genus of the base curve are arbitrary. Defining isomonodromic…
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