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}
}
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… 

Figures from this paper

PAINLEVÉ EQUATION OF TYPE VI , PART II

In this paper, we show that the family of moduli spaces of α-stable (t, λ)parabolic φ-connections of rank 2 over P with 4-regular singular points and the fixed determinant bundle of degree −1 is

Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces

In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on $\mathbb{P}^1$ and rank 2 (parabolic) Higgs bundle on $\mathbb{P}^1$. Then we

Flat rank 2 vector bundles on genus 2 curves

We study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of under- lying vector bundles (including unstable

On the cohomology of the moduli space of parabolic connections

We study the moduli space of logarithmic connections of rank 2 on $${\mathbb {P}}^1 {\setminus } \{ t_1, \dots , t_5 \}$$ P 1 \ { t 1 , ⋯ , t 5 } with fixed spectral data. The aim of this paper is to

On the Cohomology of Moduli Space of Parabolic Connetions

We study the moduli space of logarithmic connections of rank $2$ on $\mathbb{P}^1 \setminus \{ t_1, \dots, t_5 \}$ with fixed spectral data. The aim of this paper is to compute the cohomology of such

MIXED HODGE STRUCTURES OF THE MODULI SPACES OF PARABOLIC CONNECTIONS

In this paper, we investigate the mixed Hodge structures of the moduli space of $\boldsymbol{\unicode[STIX]{x1D6FC}}$ -stable parabolic Higgs bundles and the moduli space of

Moduli space of parabolic $\Lambda$-modules over a curve

Simpson, in 1994, introduced the notion of $\Lambda$-modules and constructed the corresponding moduli space, where $\Lambda$ is a sheaf of rings of differential operators. Higgs bundles, connections

Automorphism group of the moduli space of parabolic vector bundles over a curve

The main objective of this thesis is the computation of the automorphism group of the moduli space of parabolic vector bundles over a smooth complex projective curve. We will start by de ning

Foliations on the moduli space of rank two connections on the projective line minus four points

We look at natural foliations on the Painleve VI moduli space of regular connections of rank $2$ on $\pp ^1 -\{ t_1,t_2,t_3,t_4\}$. These foliations are fibrations, and are interpreted in terms of
...

References

SHOWING 1-10 OF 76 REFERENCES

Deformation of Okamoto-Painleve pairs and Painleve equations (Proceedings of the Workshop "Algebraic Geometry and Integrable Systems related to String Theory")

In this paper, we introduce the notion of generalized rational Okamoto-Painlev\'e pair (S, Y) by generalizing the notion of the spaces of initial conditions of Painlev\'e equations. After classifying

Moduli of parabolic connections on a curve and Riemann-Hilbert correspondence

Let $(C,\bt)$ ($\bt=(t_1,...,t_n)$) be an $n$-pointed smooth projective curve of genus $g$ and take an element $\blambda=(\lambda^{(i)}_j)\in\C^{nr}$ such that

On the Moduli of SL ( 2 )-bundles with Connections on P 1 \ { x 1 ,

The moduli spaces of bundles with connections on algebraic curves have been studied from various points of view (see [6], [10]). Our interest in this subject was motivated by its relation with the

Rational Surfaces Associated with Affine Root Systems¶and Geometry of the Painlevé Equations

Abstract: We present a geometric approach to the theory of Painlevé equations based on rational surfaces. Our starting point is a compact smooth rational surface X which has a unique anti-canonical

Moduli of parabolic stable sheaves on a projective scheme

T he moduli spaces o f parabolic vector bundles have been studied especially on algebraic curves ([5]). M. Maruyama and K. Yokogawa have extended the concept of parabolic sheaves to a higher

MODULI OF SEMISTABLE LOGARITHMIC CONNECTIONS

Under the Riemann Hilbert correspondence, which is an equivalence of categories, local systems on a nonsingular complex projective variety X correspond to pairs E = (s, V) where ' is a locally free

Monodromy of certain Painlevé–VI transcendents and reflection groups

Abstract.We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters β=γ=0, δ=1/2 and 2α=(2μ-1)2 with arbitrary μ, 2μ≠∈ℤ. We introduce

Orthogonality of natural sheaves on moduli stacks of SL(2)-bundles with connections on $ \Bbb P^1 $ minus 4 points

Abstract.A special kind of SL(2)-bundles with connections on $\Bbb P^1\setminus\{x_1,\dots,x_4\}$ is considered. We construct an equivalence between the derived category of quasicoherent sheaves on

Nodal curves and Riccati solutions of Painleve equations

In this paper, we study Riccati solutions of Painlev\'e equations from a view point of geometry of Okamoto-Painlev\'e pairs $(S,Y)$. After establishing the correspondence between (rational) nodal

Moduli of stable sheaves , II By

Introduction. Let S be a scheme o f finite type over a universally Japanese ring, f: X --4S be a smooth, projective, geometrically integral morphisrn and let (9,(1) be an f-very ample invertible
...