Algebraic Nahm transformation gives a holomorphic symplectic isomorphism between the rank-2 and rank-3 (JKT) Dolbeault moduli spaces for all six Painleve systems, realized by explicit elliptic fibrations of types I*_0, I*_1, eE6, eE7, eE8.
Rank three representations of Painlev\'e systems: I. Wild character varieties
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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.
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Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence
Algebraic Nahm transformation gives a holomorphic symplectic isomorphism between the rank-2 and rank-3 (JKT) Dolbeault moduli spaces for all six Painleve systems, realized by explicit elliptic fibrations of types I*_0, I*_1, eE6, eE7, eE8.