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Rank three representations of Painlevé systems: II. de Rham structure, Fourier--Laplace transformation
Miklos Eper, Szilard Szabo
We use formal microlocalization to describe the Fourier--Laplace transformation between rank 3 and rank 2 D-module representations of Painleve systems. We conclude the existence of…
Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence
Miklos Eper, Szilard Szabo
We prove that there exists a holomorphic symplectic isomorphism between the rank 2 and 3 representations of the Painleve systems in the Dolbeault complex structure, and give explic…
Rank three representations of Painlevé systems: I. Wild character varieties
Miklos Eper, Szilard Szabo
We give explicit cubic equations for the wild character varieties corresponding to the rank 3 representations of Painlevé equations, and compare them to the ones of their classical…
Asymptotic geometry of non-abelian Hodge theory and Riemann--Hilbert correspondence, rank three case
Miklos Eper, Szilard Szabo
We prove the Geometric P=W conjecture in rank 3 on the three-punctured sphere. We describe the topology at infinity of the related character variety. We use asymptotic abelianizati…
Canonical coordinates for moduli spaces of rank two irregular connections on curves
Arata Komyo, Frank Loray, Masa-Hiko Saito +1
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a ``companion'' normal form. This allow u…