Tau-Functions and Monodromy Symplectomorphisms

@article{Bertola2019TauFunctionsAM,
  title={Tau-Functions and Monodromy Symplectomorphisms},
  author={Marco Bertola and Dmitry Korotkin},
  journal={Communications in Mathematical Physics},
  year={2019},
  volume={388},
  pages={245 - 290}
}
We derive a new Hamiltonian formulation of Schlesinger equations in terms of the dynamical r-matrix structure. The corresponding symplectic form is shown to be the pullback, under the monodromy map, of a natural symplectic form on the extended monodromy manifold. We show that Fock–Goncharov coordinates are log-canonical for the symplectic form. Using these coordinates we define the symplectic potential on the monodromy manifold and interpret the Jimbo–Miwa–Ueno tau-function as the generating… 
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8 Citations
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8 Citations

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The note corrects the aforementioned paper (Bertola in Commun Math Phys 294(2):539–579, 2010). The consequences of the correction are traced and the examples updated.

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In this paper we consider the symplectic properties of the monodromy map of second order equations on a Riemann surface whose potential is meromorphic with second order poles. We show that the…
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