Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence

Miklos Eper; Szilard Szabo

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arXiv · 2509.00418

Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence

Miklos Eper·Szilard Szabo

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Abstract

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.

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Miklos Eper, Szilard Szabo. 2025-08-30. Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence. https://arxiv.org/abs/2509.00418

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