|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.