Two aspects of the theta divisor associated with the autonomous Garnier system of type 9/2

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  • Representation Theory and Differential Equations : Proceedings of JMM Workshop on Representation Theory and Differential Equations,November 26-27,2016 Josai University

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In a previous paper [16], we considered the 40 types of autonomous 4-dimensional Painlev´e-type equations and studied the degenerations of their spectral curves. In this paper, we treat the autonomous Garnier system of type 9/2, one of the most degenerated systems, as an example to illustrate another important curve (or union of curves) associated with the system:the Painlev´e divisor [2]. These curves can be considered as the theta divisor of the Liouville tori, which in turn is the Jacobian of these curves. Some of the possible applications are construction of 2 × 2 Lax pair using separation of variables [24], and making identification or distiction with other systems.

identifier:JOS-13447777-1012

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