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EPW cubes

Atanas Iliev, Grzegorz Kapustka, Michał Kapustka and Kristian Ranestad


We construct a new 20-dimensional family of projective six-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 surface and are constructed as natural double covers of special codimension-three subvarieties of the Grassmannian G(3,6). These codimension-three subvarieties are defined as Lagrangian degeneracy loci and their construction is parallel to that of EPW sextics, we call them the EPW cubes. As a consequence we prove that the moduli space of polarized IHS sixfolds of K3-type, Beauville–Bogomolov degree 4 and divisibility 2 is unirational.

Funding source: Seoul National University

Award Identifier / Grant number: 0450-20130016

Funding source: Narodowe Centrum Nauki

Award Identifier / Grant number: 2013/08/A/ST1/00312

Award Identifier / Grant number: 2013/10/E/ST1/00688

Funding source: Norges Forskningsråd

Award Identifier / Grant number: 239015

Funding statement: A. Iliev was supported by SNU grant 0450-20130016, G. Kapustka by NCN grant 2013/08/A/ST1/00312, M. Kapustka by NCN grant 2013/10/E/ST1/00688, and K. Ranestad by RCN grant 239015.


The authors wish to thank Olivier Debarre, Alexander Kuznetsov and Kieran O’Grady for useful comments, O’Grady in particular for pointing out a proof of Proposition 5.3.


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Received: 2015-11-23
Revised: 2016-06-24
Published Online: 2016-08-11
Published in Print: 2019-03-01

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