A modular group action on cubic surfaces and the monodromy of the Painlevé VI equation.

DOI10.3792/pjaa.78.131zbMath1058.34125OpenAlexW2071280318MaRDI QIDQ1869652

Katsunori Iwasaki

Publication date: 30 September 2003

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.78.131

zbMATH Keywords

Painlevé equationmodular groupbraid groupmonodromy surfacenonlinear monodromy

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Painlevé-type functions (33E17)

Related Items

Note on character varieties and cluster algebras, Surface group representations in \(\mathrm{SL}_2(\mathbb{C})\) with finite mapping class orbits, Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities, The space of monodromy data for the Jimbo-Sakai family of \(q\)-difference equations, On the monodromy manifold of \(q\)-Painlevé VI and its Riemann-Hilbert problem, An area-preserving action of the modular group on cubic surfaces and the Painlevé VI equation, A map between moduli spaces of connections, An ergodic study of Painlevé VI, Algebraic isomonodromic deformations of logarithmic connections on the Riemann sphere and finite braid group orbits on character varieties, Moduli spaces for linear differential equations and the Painlevé equations, Symmetric cubic surfaces and 𝐆₂ character varieties, Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI. I, Bers and Hénon, Painlevé and Schrödinger, Algebraic solutions of the sixth Painlevé equation, Conway topograph, -dynamics and two-valued groups, The fifty-two icosahedral solutions to Painlevé VI

Cites Work

• A modification of Cayley's family of cubic surfaces and birational action of W(\(E_ 6)\) over it
• Monodromy of certain Painlevé-VI transcendents and reflection groups
• Rational solutions of the Painlevé VI equation
• Deformation of Okamoto–Painlevé pairs and Painlevé equations
• Cross Ratio Variety as a Moduli Space of Cubic Surfaces
• The elliptic representation of the general Painlevé VI equation
• Picard and Chazy solutions to the Painlevé VI equation
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