Jacobian variety and integrable system - after Mumford, Beauville and Vanhaecke

Rei Inoue, Yukiko Konishi, Takao Yamazaki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Beauville [A. Beauville, Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta. Math. 164 (1990) 211-235] introduced an integrable Hamiltonian system whose general level set is isomorphic to the complement of the theta divisor in the Jacobian of the spectral curve. This can be regarded as a generalization of the Mumford system [D. Mumford, Tata Lectures on Theta II, Birkhäuser, 1984]. In this article, we construct a variant of Beauville's system whose general level set is isomorphic to the complement of the intersection of the translations of the theta divisor in the Jacobian. A suitable subsystem of our system can be regarded as a generalization of the even Mumford system introduced by Vanhaecke [P. Vanhaecke, Linearising two-dimensional integrable systems and the construction of action-angle variables, Math. Z. 211 (1992) 265-313; P. Vanhaecke, Integrable systems in the realm of algebraic geometry, in: Lecture Notes in Mathematics, vol. 1638, 2001].

Original languageEnglish
Pages (from-to)815-831
Number of pages17
JournalJournal of Geometry and Physics
Volume57
Issue number3
DOIs
Publication statusPublished - 2007 Feb 1

Keywords

  • Completely integrable system
  • Jacobian variety
  • Mumford system
  • Spectral curve

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Jacobian variety and integrable system - after Mumford, Beauville and Vanhaecke'. Together they form a unique fingerprint.

  • Cite this