Distinguished lectures
Hyper-Kähler manifolds
Speaker: Claire Voisin (Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)Date: Friday, 01 April 2022 - 11:00-13:30Place: Aula Azul, ICMAT
Online: youtu.be/AIATBTQ-KjQ
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 introduce them and describe some of their general properties, from the viewpoints of Riemannian geometry, topology, and algebraic geometry. The second lecture will focus on dimension 4. I will describe a simple topological characterization of hyper-Kähler manifolds of Hilb^2(K3) deformation type and sketch the proof (this is joint work with Debarre, Huybrechts, and Macrì).
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