Algebraic complete integrability of an integrable system of Beauville

Jun-Muk Hwang[1]; Yasunari Nagai[1]

  • [1] Korea Institute for Advanced Study (KIAS) 207-43 Cheongnyangni 2-dong Dongdaemun-gu, Seoul 130-722 (Korea)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 2, page 559-570
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Hwang, Jun-Muk, and Nagai, Yasunari. "Algebraic complete integrability of an integrable system of Beauville." Annales de l’institut Fourier 58.2 (2008): 559-570. <http://eudml.org/doc/10324>.

@article{Hwang2008,
abstract = {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.},
affiliation = {Korea Institute for Advanced Study (KIAS) 207-43 Cheongnyangni 2-dong Dongdaemun-gu, Seoul 130-722 (Korea); Korea Institute for Advanced Study (KIAS) 207-43 Cheongnyangni 2-dong Dongdaemun-gu, Seoul 130-722 (Korea)},
author = {Hwang, Jun-Muk, Nagai, Yasunari},
journal = {Annales de l’institut Fourier},
keywords = {Integrable system; moduli space of stable sheaves; surface; Lagrangian fibration; integrable system},
language = {eng},
number = {2},
pages = {559-570},
publisher = {Association des Annales de l’institut Fourier},
title = {Algebraic complete integrability of an integrable system of Beauville},
url = {http://eudml.org/doc/10324},
volume = {58},
year = {2008},
}

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
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 2
SP - 559
EP - 570
AB - 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.
LA - eng
KW - Integrable system; moduli space of stable sheaves; surface; Lagrangian fibration; integrable system
UR - http://eudml.org/doc/10324
ER -

References

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  1. Arnaud Beauville, Vector bundles on the cubic threefold, Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000) 312 (2002), 71-86, Amer. Math. Soc., Providence, RI Zbl1056.14059MR1941574
  2. Stéphane Druel, 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 19 (2000), 985-1004 Zbl1024.14004MR1792346
  3. Daniel Huybrechts, Manfred Lehn, The Geometry of Moduli Spaces of Sheaves, (1997), Friedr. Vieweg & Sohn, Braunschweig Zbl0872.14002MR1450870
  4. Frances Clare Kirwan, Partial desingularisations of quotients of nonsingular varieties and their Betti numbers, Ann. of Math. (2) 122 (1985), 41-85 Zbl0592.14011MR799252
  5. Manfred Lehn, Christoph Sorger, La singularité de O’Grady, J. Alg. Geom. 15 (2006), 753-770 Zbl1156.14030
  6. Shigeru Mukai, Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface, Invent. Math. 77 (1984), 101-116 Zbl0565.14002MR751133
  7. Kieran G. O’Grady, Desingularized moduli spaces of sheaves on a K 3 , J. Reine Angew. Math. 512 (1999), 49-117 Zbl0928.14029

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