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

2008/06/14 by Rei Inoue, Inoue, Rei, Pol Vanhaecke +3
Mathematics · Physics and Astronomy · #14H40 #14H70 #37J35 #53D17 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0806.2362

openalex publication_date 2008/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the singular iso-level manifold M_g(0) of the genus g Mumford system associated to the spectral curve y²=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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