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arXiv · 1910.14168

Uniqueness of polarization for the autonomous 4-dimensional Painlevé-type systems

Akane Nakamura·Eric Rains
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Abstract

We prove that for any autonomous 4-dimensional integral system of Painlevé type, the Jacobian of the generic spectral curve has a unique polarization, and thus by Torelli's theorem cannot be isomorphic as an unpolarized abelian surface to any other Jacobian. This enables us to identify the spectral curve and any irreducible genus two component of the boundary of an affine patch of the Liouville torus.

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Akane Nakamura, Eric Rains. 2019-10-30. Uniqueness of polarization for the autonomous 4-dimensional Painlevé-type systems. https://arxiv.org/abs/1910.14168

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