no. 2
Algebraic complete integrability of an integrable system of Beauville
[Complète intégrabilité algébrique d’un système intégrable de Beauville]
Hwang, Jun-Muk1 ; Nagai, Yasunari1
1 Korea Institute for Advanced Study (KIAS) 207-43 Cheongnyangni 2-dong Dongdaemun-gu, Seoul 130-722 (Korea)
Annales de l'Institut Fourier, Tome 58 (2008) no. 2, pp. 559-570.

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.

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.

DOI : 10.5802/aif.2360
Classification : 14J60, 37J35
Keywords: Integrable system, moduli space of stable sheaves
Mot clés : sytème intégrable, espace des modules de faisceaux stables

Hwang, Jun-Muk 1 ; Nagai, Yasunari 1

1 Korea Institute for Advanced Study (KIAS) 207-43 Cheongnyangni 2-dong Dongdaemun-gu, Seoul 130-722 (Korea) 
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Hwang, Jun-Muk; Nagai, Yasunari. Algebraic complete integrability of an integrable system of Beauville. Annales de l'Institut Fourier, Tome 58 (2008) no. 2, pp. 559-570. doi : 10.5802/aif.2360. https://aif.centre-mersenne.org/articles/10.5802/aif.2360/

[1] Beauville, Arnaud Vector bundles on the cubic threefold, Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000) (Contemp. Math.), Volume 312, Amer. Math. Soc., Providence, RI, 2002, pp. 71-86 | MR | Zbl

[2] Druel, Stéphane Espace des modules de faisceaux de rang 2 semi-stables de classes de Chern c 1 =0,c 2 =2 et c 3 =0 sur la cubique de ℙ 4 , Internat. Math. Res. Notices, Volume 19 (2000), pp. 985-1004 | DOI | MR | Zbl

[3] Huybrechts, Daniel; Lehn, Manfred The Geometry of Moduli Spaces of Sheaves, Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997 | MR | Zbl

[4] Kirwan, Frances Clare Partial desingularisations of quotients of nonsingular varieties and their Betti numbers, Ann. of Math. (2), Volume 122 (1985) no. 1, pp. 41-85 | DOI | MR | Zbl

[5] Lehn, Manfred; Sorger, Christoph La singularité de O’Grady, J. Alg. Geom., Volume 15 (2006) no. 4, pp. 753-770 | DOI | Zbl

[6] Mukai, Shigeru Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math., Volume 77 (1984) no. 1, pp. 101-116 | DOI | MR | Zbl

[7] O’Grady, Kieran G. Desingularized moduli spaces of sheaves on a K3, J. Reine Angew. Math., Volume 512 (1999), pp. 49-117 | DOI | Zbl

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