Home > Proceedings > Adv. Stud. Pure Math. > Moduli Spaces and Arithmetic Geometry (Kyoto, 2004) > Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI, part II
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VOL. 45 | 2006 Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI, part II
Michi-aki Inaba, Katsunori Iwasaki, Masa-Hiko Saito

Editor(s) Shigeru Mukai, Yoichi Miyaoka, Shigefumi Mori, Atsushi Moriwaki, Iku Nakamura

## Abstract

In this paper, we show that the family of moduli spaces of $\boldsymbol{\alpha}'$-stable $(\mathbf{t}, \boldsymbol{\lambda})$-parabolic $\phi$-connections of rank 2 over $\mathbf{P}^1$ with 4-regular singular points and the fixed determinant bundle of degree $-1$ is isomorphic to the family of Okamoto–Painlevé pairs introduced by Okamoto [O1] and [STT]. 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 flows on the family of moduli space of stable parabolic connections via the Riemann-Hilbert correspondences, we will show that a property of the Riemann-Hilbert correspondences implies the Painlevé property of isomonodromic flows.

## Information

Published: 1 January 2006
First available in Project Euclid: 3 January 2019

zbMATH: 1115.14005
MathSciNet: MR2310256

Digital Object Identifier: 10.2969/aspm/04510387