EPW Cubes
Journal article, Peer reviewed
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2016-08Metadata
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Iliev, A., Kaputska, G., Kaputska, M. et al. (2016) EPW Cubes. Journal fur die reine und angewandte mathematik, 2019(748) 10.1515/crelle-2016-0044Abstract
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.