|Dept.||Univ. of Stavanger, Norway|
I will report on joint work with A. Iliev, G. Kapustka, K. Ranestad. 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. They 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 can be seen as generalizations of EPW sextics, we call them the EPW cubes.