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arXiv · 2003.10984

On the period of Lehn, Lehn, Sorger, and van Straten's symplectic eightfold

Nicolas Addington·Franco Giovenzana
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Abstract

For the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane, we show that a natural Abel-Jacobi map from H^4_prim(Y) to H^2_prim(Z) is a Hodge isometry. We describe the full H^2(Z) in terms of the Mukai lattice of the K3 category A of Y. We give numerical conditions for Z to be birational to a moduli space of sheaves on a K3 surface or to Hilb^4(K3). We propose a conjecture on how to use Z to produce equivalences from A to the derived category of a K3 surface.

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Nicolas Addington, Franco Giovenzana. 2020-03-24. On the period of Lehn, Lehn, Sorger, and van Straten's symplectic eightfold. https://doi.org/10.1215/21562261-2022-0033

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