We show that the Beauville’s integrable system on a ten dimensional moduli space of sheaves on a K3 surface constructed via a moduli space of stable sheaves on cubic threefolds is algebraically completely integrable, using O’Grady’s construction of a symplectic resolution of the moduli space of sheaves on a K3.
Nous montrons que le système intégrable de Beauville sur un espace de dimension dix de modules de faisceaux sur une surface K3 construit par un espace de modules de faisceaux stables sur les cubiques de dimension trois est algébriquement complètement intégrable. Nous utilisons la construction d’O’Grady d’une résolution symplectique de l’espace des modules de faisceaux sur une surface K3.
Keywords: Integrable system, moduli space of stable sheaves
Mot clés : sytème intégrable, espace des modules de faisceaux stables
@article{AIF_2008__58_2_559_0, author = {Hwang, Jun-Muk and Nagai, Yasunari}, title = {Algebraic complete integrability of an integrable system of {Beauville}}, journal = {Annales de l'Institut Fourier}, pages = {559--570}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2360}, zbl = {1144.14037}, mrnumber = {2410382}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2360/} }
TY - JOUR AU - Hwang, Jun-Muk AU - Nagai, Yasunari TI - Algebraic complete integrability of an integrable system of Beauville JO - Annales de l'Institut Fourier PY - 2008 SP - 559 EP - 570 VL - 58 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2360/ DO - 10.5802/aif.2360 LA - en ID - AIF_2008__58_2_559_0 ER -
%0 Journal Article %A Hwang, Jun-Muk %A Nagai, Yasunari %T Algebraic complete integrability of an integrable system of Beauville %J Annales de l'Institut Fourier %D 2008 %P 559-570 %V 58 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2360/ %R 10.5802/aif.2360 %G en %F AIF_2008__58_2_559_0
Hwang, Jun-Muk; Nagai, Yasunari. Algebraic complete integrability of an integrable system of Beauville. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 559-570. doi : 10.5802/aif.2360. http://www.numdam.org/articles/10.5802/aif.2360/
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