Nodal curves and Riccati solutions of Painlevé equations

DOI10.1215/kjm/1250283083zbMath1117.14015OpenAlexW1530166346MaRDI QIDQ816492

Hitomi Terajima, Masa-Hiko Saito

Publication date: 9 March 2006

Published in: Journal of Mathematics of Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/kjm/1250283083

zbMATH Keywords

Painlevé equationlocal cohomologyRiccati solutionnodal curveOkamoto-Painlevé pair

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relationships between algebraic curves and integrable systems (14H70) Formal methods and deformations in algebraic geometry (14D15) Deformations of submanifolds and subspaces (32G10)

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The Hermite-Krichever ansatz for Fuchsian equations with applications to the sixth Painlevé equation and to finite-gap potentials ⋮ Isomonodromy for the degenerate fifth Painlevé equation ⋮ Families of Okamoto-Painlevé pairs and Painlevé equations ⋮ Finite branch solutions to Painlevé VI around a fixed singular point ⋮ Moduli spaces for linear differential equations and the Painlevé equations ⋮ Dynamics on character varieties and Malgrange irreducibility of Painlevé VI equation ⋮ The Lamé family of connections on the projective line ⋮ On the moduli spaces of framed logarithmic connections on a Riemann surface ⋮ A Riemann–Hilbert approach to Painlevé IV

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