Zeros of the Jimbo, Miwa, Ueno tau function

Details Zeros of the Jimbo, Miwa, Ueno tau function Zeros of the Jimbo, Miwa, Ueno tau function

1998-10-06

arxiv.org/abs/solv-int/9810004v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

59 pages

Scientific paper

10.1063/1.533112

We introduce a family of local deformations for meromorphic connections on the Riemann sphere in the neighborhood of a higher rank (simple) singularity. Following a scheme introduced by Malgrange we use these local models to prove that the zeros of the tau function introduced by Jimbo, Miwa and Ueno occur precisely at those points in the deformation space at which a certain Birkhoff-Riemann- Hilbert problem fails to have a solution.

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