Description
18 June 2020 (Thursday), 14:00 GMT
Speaker: Claire Voisin (Paris, France)
Title: Triangle varieties and surface decomposition of hyper-Kahler manifolds
Abstract: In recent years, new constructions of complete families of
polarized hyper-Kahler manifolds have been found starting from Fano
geometry. These hyper-Kahler manifolds also appear as general deformations
of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will introduce
the notion of surface decomposition for a variety X with a nontrivial
Hodge structure on degree 2 cohomology. I will show that this notion is
restrictive topologically, as it implies Beauville-Fujiki type relations.
I will also show the existence of such a surface decomposition for the
general hyper-Kahler manifolds mentioned above. This has interesting
consequences on Beauville's conjecture on the Chow ring of hyper-Kahler
manifolds.
Zoom link:
https://us02web.zoom.us/j/9918493831?pwd=NzJNWmd5Y2h2eXFqbGpiN3Fva1pYQT09
Zoom meeting ID: 991 849 3831
Password: 16-18-June
Host: Chenyang Xu