Geodesic
Symplectic structure on a~moduli space of sheaves on the cubic fourfold
Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 121-144

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We construct a 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold in the 5-dimensional projective space. It parametrizes the stable rank 2 vector bundles on hyperplane sections of the cubic 4-fold which are obtained by the Serre construction from normal elliptic quintics. The natural projection of this moduli space onto the dual projective 5-space is a Lagrangian fibration. The symplectic structure is closely related (and conjecturally equal) to the quasi-symplectic structure induced by the Yoneda pairing on the moduli space. 
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     author = {D. G. Markushevich and A. S. Tikhomirov},
     title = {Symplectic structure on a~moduli space of sheaves on the cubic fourfold},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_1_a6/}
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D. G. Markushevich; A. S. Tikhomirov. Symplectic structure on a~moduli space of sheaves on the cubic fourfold. Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 121-144. http://geodesic.mathdoc.fr/item/IM2_2003_67_1_a6/