Isomonodromic deformation of Fuchsian projective connections on elliptic curves

DOI10.1017/S002776300002554XzbMath1055.32012MaRDI QIDQ4457782

Shingo Kawai

Publication date: 17 March 2004

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

elliptic curveHamiltonian systemsymplectic structureisomonodromic deformationFuchsian system

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Symplectic structures of moduli spaces (53D30) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34)

Related Items (4)

On the moduli of logarithmic connections on elliptic curves ⋮ An area-preserving action of the modular group on cubic surfaces and the Painlevé VI equation ⋮ Studies on monodromy preserving deformation of linear differential equations on elliptic curves ⋮ Hamiltonian system for the elliptic form of Painlevé VI equation

Cites Work

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• The symplectic nature of fundamental groups of surfaces
• Fuchsian moduli on a Riemann surface --- Its Poisson structure and Poincaré-Lefschetz duality
• Gaudin model, KZ equation and an isomonodromic problem on the torus
• The symplectic nature of the space of projective connections on Riemann surfaces
• PRINCIPAL BUNDLES ON OPEN SURFACES AND INVARIANT FUNCTIONS ON LIE GROUPS
• Elliptic Calogero–Moser systems and isomonodromic deformations
• ON THE HOLONOMIC DEFORMATION OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS ON AN ELLIPTIC CURVE

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