Аннотация:
In recent years, new constructions of complete families of polarized
hyper-Kähler manifolds have been found starting from Fano geometry.
These hyper-Kähler manifolds also appear as deformations of Hilbert
schemes of K3 surfaces or O'Grady manifolds. I will introduce the notion
of surface decomposition, which is restrictive and gives a geometric
explanation for the Beauville-Fujiki relations, and I will show the existence
of such a surface decomposition for the general hyper-Kähler
manifold mentioned above. This has implications on the Beauville conjecture.