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

Rei Inoue, Pol Vanhaecke, Takao Yamazaki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the singular isolevel manifold Mg (0) of the genus g Mumford system associated to the spectral curve y2 = x2g+1. We show that Mg (0) is stratified by g +1 open subvarieties of additive algebraic groups of dimension 0,1....g, and we give an explicit description of Mg (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.

Original languageEnglish
Pages (from-to)508-532
Number of pages25
JournalCommunications on Pure and Applied Mathematics
Volume63
Issue number4
DOIs
Publication statusPublished - 2010 Apr 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Singular fiber of the Mumford system and rational solutions to the KdV hierarchy'. Together they form a unique fingerprint.

Cite this