Hyperelliptic Prym varieties and integrable systems

Rui Loja Fernandes, Pol Vanhaecke

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce two algebraic completely integrable analogues of the Mumford systems which we call hyperelliptic Prym systems, because every hyperelliptic Prym variety appears as a fiber of their momentum map. As an application we show that the general fiber of the momentum map of the periodic Volterra lattice ȧi = ai (ai-1 - ai+1), i = 1,⋯,n, an+1 = a1, is an affine part of a hyperelliptic Prym variety, obtained by removing n translates of the theta divisor, and we conclude that this integrable system is algebraic completely integrable.

Original languageEnglish (US)
Pages (from-to)169-196
Number of pages28
JournalCommunications in Mathematical Physics
Volume221
Issue number1
DOIs
StatePublished - Jul 2001
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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