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arXiv · 1404.5657

On the symplectic eightfold associated to a Pfaffian cubic fourfold

N. Addington·M. Lehn
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Abstract

We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of complexes on X and observe that at some point of Z, hence on a Zariski open subset, the complex is just the ideal sheaf of four points.

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N. Addington, M. Lehn. 2014-04-22. On the symplectic eightfold associated to a Pfaffian cubic fourfold. https://doi.org/10.1515/crelle-2014-0145

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