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Singular fiber of the Mumford system and rational solutions to the KdV hierarchy
Author(s) -
Inoue Rei,
Yamazaki Takao,
Vanhaecke Pol
Publication year - 2010
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20310
Subject(s) - mathematics , compactification (mathematics) , jacobian matrix and determinant , genus , pure mathematics , algebraic geometry , dimension (graph theory) , algebraic number , manifold (fluid mechanics) , conjecture , hierarchy , algebra over a field , mathematical analysis , market economy , mechanical engineering , botany , economics , engineering , biology
We study the singular isolevel manifold M g (0) of the genus g Mumford system associated to the spectral curve y 2 = x 2 g + 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. © 2009 Wiley Periodicals, Inc.