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      EPW Cubes

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          Abstract

          We construct a new 20-dimensional family of projective 6-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 3 subvarieties of the Grassmanian G(3,6). These codimension 3 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.

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          Author and article information

          Journal
          2015-05-10
          2016-07-13
          Article
          1505.02389
          c7bd4a69-5083-40fb-8b44-6e4c85a69a12

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          14J10, 14J40
          minor corrections, 25 pages, to appear in J. Reine Angew. Math
          math.AG

          Geometry & Topology
          Geometry & Topology

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