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

Rei Inoue, Pol Vanhaecke, Takao Yamazaki

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…