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arXiv · 1810.01224

Sato Grassmannian and Degenerate Sigma Function

Julia Bernatska·Victor Enolski·Atsushi Nakayashiki
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Abstract

The degeneration of the hyperelliptic sigma function is studied. We use the Sato Grassmannian for this purpose. A simple decomposition of a rational function gives a decomposition of Pl\"ucker coordinates of a frame of the Sato Grassmannian. It then gives a decomposition of the tau function corresponding to the degeneration of a hyperelliptic curve of genus $g$ in terms of the tau functions corresponding to a hyperelliptic curve of genus $g-1$. Since the tau functions are described by sigma functions, we get the corresponding formula for the degenerate hyperelliptic sigma function.

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Julia Bernatska, Victor Enolski, Atsushi Nakayashiki. 2018-10-02. Sato Grassmannian and Degenerate Sigma Function. https://doi.org/10.1007/s00220-020-03704-5

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