The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces. (March 2013) - Charles, François; Markman, Eyal
Abstract We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky's theory of hyperholomorphic sheaves and a study of the cohomology algebra of Hilbert schemes of K3 surfaces.