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Explore the fundamental concepts of hyper-Kähler manifolds in this comprehensive lecture delivered by Claire Voisin from the French National Centre for Scientific Research at the University of Miami. Delve into the special class of compact Kähler manifolds with trivial canonical bundle, understanding their role as higher-dimensional generalizations of K3 surfaces. Discover how various deformation classes of hyper-Kähler manifolds can be constructed from K3 or abelian surfaces. Examine the main general classical properties of hyper-Kähler manifolds, laying the groundwork for a more focused discussion on four-dimensional manifolds in the subsequent lecture. Gain insights into the topological characterization of hyper-Kähler manifolds of Hilb2(K3) deformation type, based on joint work with Debarre, Huybrechts, and Macrì.
