Hyper-Kähler Manifolds - Part 2

Delve into the advanced mathematical realm of hyper-Kähler manifolds in this second part of a lecture series delivered by Claire Voisin from the French National Centre for Scientific Research at the University of Miami. Explore the intricacies of these special compact Kähler manifolds with trivial canonical bundles, which serve as higher-dimensional generalizations of K3 surfaces. Examine how various deformation classes of hyper-Kähler manifolds can be constructed from K3 or abelian surfaces. Focus on four-dimensional hyper-Kähler manifolds and gain insights into the proof of a simple topological characterization of hyper-Kähler manifolds of Hilb2(K3) deformation type, based on joint work with Debarre, Huybrechts, and Macrì. Enhance your understanding of complex geometry and algebraic topology through this in-depth, 72-minute exploration of cutting-edge mathematical concepts.