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It is proven that the composition of the Yoneda coupling with the semiregularity map is a closed 2-form on moduli spaces of sheaves. Two examples are given when this 2-form is symplectic. Both of them are moduli spaces of torsion sheaves on the cubic 4-fold Y. The first example is the Fano scheme of lines in Y. Beauville and Donagi showed that it is symplectic but did not construct an explicit symplectic...
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