Distinguished lecture information

Distinguished lectures

Hyper-Kähler manifolds

Speaker:  Claire Voisin (Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)
Date:  Friday, 01 April 2022 - 11:00-13:30
Place:  Aula Azul, ICMAT
Online:  youtu.be/AIATBTQ-KjQ


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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