Mathematics > Algebraic Geometry
[Submitted on 30 Aug 2025
]
Title: Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence
Title: 三阶Painleve系统的表示：III. Dolbeault结构，谱对应
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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