Singular fiber of the Mumford system and rational solutions to the KdV hierarchy

Details Singular fiber of the Mumford system and rational solutions to the KdV hierarchy Singular fiber of the Mumford system and rational solutions to the KdV hierarchy

2008-06-14

arxiv.org/abs/0806.2362v3

Physics

Mathematical Physics

21 pages

Scientific paper

We study the singular iso-level manifold $M_g(0)$ of the genus $g$ Mumford system associated to the spectral curve $y^2=x^{2g+1}$. We show that $M_g(0)$ is stratified by $g+1$ open subvarieties of additive algebraic groups of dimension $0,1,...,g$ and we give an explicit description of $M_g(0)$ in terms of the compactification of the generalized Jacobian. As a consequence, we obtain an effective algorithm to compute rational solutions to the genus $g$ Mumford system, which is closely related to rational solutions of the KdV hierarchy.

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