Moduli of Stable Parabolic Connections, Riemann-Hilbert Correspondence and Geometry of Painlevé Equation of Type VI, Part II

Simple item page
dc.creatorInaba, Michi-aki
dc.creatorIwasaki, Katsunori
dc.creatorSaito, Masa-Hiko
dc.date2006-04-30
dc.date2007-02-21
dc.date.accessioned2026-07-07T07:47:47Z
dc.date.available2026-07-07T07:47:47Z
dc.descriptionIn this paper, we show that the family of moduli spaces of $\balpha'$-stable $(\bt, \blambda)$-parabolic $ϕ$-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--Painlevé 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 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.
dc.description29 pages, 1 figures, Adv. Stud. Pure Math., 45, 2006, Proceedings of Moduli spaces and Arithmetic Geometry (Kyoto, 2004)
dc.identifierhttps://arxiv.org/abs/math/0605025
dc.identifierhttp://arxiv.org/abs/math/0605025
dc.identifierAdv. Stud. Pure Math., 45, 2006, 387--432
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124284
dc.subjectAlgebraic Geometry
dc.subjectClassical Analysis and ODEs
dc.subject34M55, 14D20, 32G34, 34G34, 58F05
dc.titleModuli of Stable Parabolic Connections, Riemann-Hilbert Correspondence and Geometry of Painlevé Equation of Type VI, Part II
dc.typetext

Files

Collections

arXiv