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.
Hirzebruch: ¨Uber vierdimensionale Riemannsche Fl¨ achen mehrdeutiger analytischer Functionen von zwei complexen Ver¨ anderlichen,Math
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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.