There are not many known examples of compact irreducible hyperkahler manifolds. Two series of examples appear in dimension 2n, for every n>1, and are related to the Hilbert scheme of points on a K3 or an abelian surface; and in dimension 6 and 10 there is one extra, or exceptional, deformation class, each of which was found by O'Grady. While considerable work has been devoted to studying hyperkahler manifolds belonging to the first two deformation classes, not much is known for the exceptional deformation classes. In this talk I will present joint work with Giovanni Mongardi and Antonio Rapagnetta, regarding the geometry of O'Grady's six dimensional example. By realizing these examples as "quotients" of another hyperkahler manifold by a birational involution, we are able to compute the Hodge numbers and, in work in progress, also study properties of their moduli spaces/deformation class.
Speaker(s): Giulia Sacca (Stony Brook University)