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Symplectic structure on a moduli space of sheaves on the cubic fourfold

D. Markushevich·A. S. Tikhomirov
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Abstract

A 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold is constructed. It parametrizes the stable rank 2 vector bundles on the hypeplane sections of the cubic 4-fold which are obtained by Serre's construction from normal elliptic quintics. The natural projection to the dual projective 5-space parametrizing the hyperplane sections is a Lagrangian fibration. The symplectic structure is closely related (and conjecturally, is equal) to the quasi-symplectic one, induced by the Yoneda pairing on the moduli space.

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D. Markushevich, A. S. Tikhomirov. 1999-10-13. Symplectic structure on a moduli space of sheaves on the cubic fourfold. https://arxiv.org/abs/math/9910063

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