Hyper-Kähler Manifolds

Abstract: Hyper-Kähler manifolds form a special class of compact Kähler manifolds with trivial canonical bundle. They are higher-dimensional generalizations of K3 surfaces, and a number of deformation classes of hyper-Kähler manifolds can be constructed starting from either a K3 or an abelian surface. In the first lecture, I will describe the main general classical properties of hyper-Kähler manifolds that will be needed in the second lecture, where I will focus to dimension 4 and sketch the proof of a simple topological characterization of hyper-Kähler manifolds of Hilb2(K3) deformation type (joint work with Debarre, Huybrechts, and Macrì).