arXiv subjects
Publications and source records attributed to Miklos Eper.
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 biregular morphism between the corresponding de Rham complex structures.
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 explicit descriptions of the corresponding elliptic fibrations. This, combined with the de Rham description given in part II, implies that the corresponding moduli spaces are hyperKaehler isometric to each other.
We give explicit cubic equations for the wild character varieties corresponding to the rank 3 representations of Painlev\'e equations, and compare them to the ones of their classical rank 2 representations.
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 abelianization of harmonic bundles away from the ramification divisor and an equivariant approach near the branch points to find the WKB (also known as Liouville--Green or phase-integral) expansion of the involved maps. We analyze the Stokes phenomenon governing their behavior.