Sato Grassmannian and Degenerate Sigma Function

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 Plücker 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.

arXiv comment28 pages

References in corpus (6)

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• On higher genus Weierstrass sigma-function
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• Sigma, tau and Abelian functions of algebraic curves
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Cited by in corpus (4)

• KdV breathers on a cnoidal wave background
• Tau Functions of (n,1) curves and Soliton Solutions on Non-Zero Constant Backgrounds
• Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk
• Hurwitz integrality of the power series expansion of the sigma function for a telescopic curve