TY - JOUR
T1 - Hyperelliptic Prym varieties and integrable systems
AU - Fernandes, Rui Loja
AU - Vanhaecke, Pol
N1 - Copyright:
Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2001/7
Y1 - 2001/7
N2 - 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.
AB - 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.
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U2 - 10.1007/s002200100476
DO - 10.1007/s002200100476
M3 - Article
AN - SCOPUS:0035600041
SN - 0010-3616
VL - 221
SP - 169
EP - 196
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -