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VOL. 59 | 2010 Hitchin integrable systems, deformations of spectral curves, and KP-type equations
Andrew R. Hodge, Motohico Mulase

Editor(s) Masa-Hiko Saito, Shinobu Hosono, Kōta Yoshioka


An effective family of spectral curves appearing in Hitchin fibrations is determined. Using this family the moduli spaces of stable Higgs bundles on an algebraic curve are embedded into the Sato Grassmannian. We show that the Hitchin integrable system, the natural algebraically completely integrable Hamiltonian system defined on the Higgs moduli space, coincides with the KP equations. It is shown that the Serre duality on these moduli spaces corresponds to the formal adjoint of pseudo-differential operators acting on the Grassmannian. From this fact we then identify the Hitchin integrable system on the moduli space of $Sp_{2m}$-Higgs bundles in terms of a reduction of the KP equations. We also show that the dual Abelian fibration (the SYZ mirror dual) to the $Sp_{2m}$-Higgs moduli space is constructed by taking the symplectic quotient of a Lie algebra action on the moduli space of $GL$-Higgs bundles.


Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1233.14026
MathSciNet: MR2683206

Digital Object Identifier: 10.2969/aspm/05910031

Primary: 14H60
Secondary: 14H70, 35Q53, 37J35

Rights: Copyright © 2010 Mathematical Society of Japan


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