En utilisant des résultats de A. Beauville (Acta Math. 164 (1990) 211–235), nous donnons une description explicite des champs de vecteurs invariants par translation sur les jacobiennes affines des courbes spectrales qui justifie mathématiquement les travaux de F.A. Smirnov and V. Zeitlin (preprint math-ph/0203037). Dans le cas hyperelliptique, cette description est due à D. Mumford (Tata Lectures on Theta, Vol. II, Birkhäuser, Boston, 1983).
Thanks to results of A. Beauville (Acta Math. 164 (1990) 211–235), we give an explicit description of translation-invariant vector fields on affine Jacobians of spectral curves, which gives a mathematical support for the work of F.A. Smirnov and V. Zeitlin (preprint math-ph/0203037). In the hyperelliptic case, this description is due to D. Mumford (Tata Lectures on Theta, Vol. II, Birkhäuser, Boston, 1983).
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@article{CRMATH_2003__337_2_105_0,
author = {Fu, Baohua},
title = {Champs de vecteurs invariants par translation sur les jacobiennes affines des courbes spectrales},
journal = {Comptes Rendus. Math\'ematique},
pages = {105--110},
publisher = {Elsevier},
volume = {337},
number = {2},
year = {2003},
doi = {10.1016/S1631-073X(03)00283-8},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00283-8/}
}
TY - JOUR AU - Fu, Baohua TI - Champs de vecteurs invariants par translation sur les jacobiennes affines des courbes spectrales JO - Comptes Rendus. Mathématique PY - 2003 SP - 105 EP - 110 VL - 337 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00283-8/ DO - 10.1016/S1631-073X(03)00283-8 LA - fr ID - CRMATH_2003__337_2_105_0 ER -
%0 Journal Article %A Fu, Baohua %T Champs de vecteurs invariants par translation sur les jacobiennes affines des courbes spectrales %J Comptes Rendus. Mathématique %D 2003 %P 105-110 %V 337 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00283-8/ %R 10.1016/S1631-073X(03)00283-8 %G fr %F CRMATH_2003__337_2_105_0
Fu, Baohua. Champs de vecteurs invariants par translation sur les jacobiennes affines des courbes spectrales. Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 105-110. doi : 10.1016/S1631-073X(03)00283-8. http://www.numdam.org/articles/10.1016/S1631-073X(03)00283-8/
[1] Completely integrable systems, Euclidean Lie algebras, and curves, Adv. Math., Volume 38 (1980), pp. 267-317
[2] Linearization of Hamiltonian systems, Jacobi varieties and representation theory, Adv. Math., Volume 38 (1980), pp. 318-379
[3] Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta Math., Volume 164 (1990), pp. 211-235
[4] Spectral covers, algebraically completely integrable, Hamiltonian systems, and moduli of bundles, Integrable Systems and Quantum Groups, Montecatini Terme, 1993, Lecture Notes in Math., 1620, Springer, Berlin, 1996, pp. 1-119
[5] Generalized Jacobians of spectral curves and completely integrable systems, Math. Z., Volume 230 (1999), pp. 487-508
[6] Linearizing flow and a cohomological interpretation of Lax equations, Amer. J. Math., Volume 107 (1985), pp. 1445-1483
[7] The spectrum of difference operators and algebraic curves, Acta Math., Volume 143 (1979), pp. 93-154
[8] Tata Lectures on Theta, Vol. II, Birkhäuser, Boston, 1983
[9] An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related nonlinear equation, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Book Store, Tokyo, 1978, pp. 115-153
[10] A. Nakayashiki, On the cohomology of theta divisors of hyperelliptic Jacobians, Preprint, | arXiv
[11] Euler characteristics of theta divisors of Jacobians for spectral curves, The Kowalevski property (Leeds, 2000), CRM Proc. Lecture Notes, 32, American Mathematical Society, Providence, RI, 2002, pp. 239-246
[12] F.A. Smirnov, V. Zeitlin, Affine Jacobians of spectral curves and integrable models, Preprint, | arXiv
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