EPW Cubes
Algebraic Geometry
2016-07-14 v2
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.
Keywords
Cite
@article{arxiv.1505.02389,
title = {EPW Cubes},
author = {Atanas Iliev and Grzegorz Kapustka and Michal Kapustka and Kristian Ranestad},
journal= {arXiv preprint arXiv:1505.02389},
year = {2016}
}
Comments
minor corrections, 25 pages, to appear in J. Reine Angew. Math