Uniqueness of polarization for the autonomous 4-dimensional Painlev\'e-type systems
Classical Analysis and ODEs
2019-11-01 v1 Algebraic Geometry
Abstract
We prove that for any autonomous 4-dimensional integral system of Painlev\'e 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.
Keywords
Cite
@article{arxiv.1910.14168,
title = {Uniqueness of polarization for the autonomous 4-dimensional Painlev\'e-type systems},
author = {Akane Nakamura and Eric Rains},
journal= {arXiv preprint arXiv:1910.14168},
year = {2019}
}