Geometry of the space of monodromy data

2023/01/10 by Jean-Pierre Ramis, Ramis, Jean-Pierre, Jacques Sauloy +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2301.04083

Abstract

In a paper published by the Annales de la Faculté de Sciences de Toulouse, with Yousuke Ohyama, we defined and studied a space of monodromy data underlying the well known derivation of q-Painlevé VI equation from q-isomonodromy conditions by Jimbo and Sakai. In a recent ArXiv preprint, Nalini Joshi and Pieter Roffelsen pursued our work. However, both our article and their preprint are ambiguous on some foundational algebro-geometric matters. We proceed here to provide sound bases.

Related

• The space of monodromy data for the Jimbo-Sakai family of q-difference\n equations
• The wild monodromy of the Fifth Painlevé equation and its action on wild character variety: an approach of confluence
• On the monodromy manifold of q-Painlevé VI and its Riemann-Hilbert problem
• Inverse Problem for semisimple Frobenius Manifolds, Monodromy Data and the Painleve' VI Equation
• Holomorphic dynamics, Painlevé VI equation and Character Varieties