Séminaire Géométries ICJ

Generalized Kuga-Satake construction for hyperkähler manifolds

Name: Generalized Kuga-Satake construction for hyperkähler manifolds
Start: 2019-03-15T10:30:00+01:00
End: 2019-03-15T11:30:00+01:00
Location: ICJ

par Nikon Kurnosov

vendredi 15 mars 2019, 10:30 → 11:30 Europe/Paris

112 (ICJ)

112

ICJ

1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua

Description

Cohomology algebra of hyperkähler manifolds is Frobenius algebra and the total Lie algebra of Lefschetz sl(2)-triples acting on it is so(4,b_2-2) by results of Loojenga-Lunts and Verbitsky. I will discuss the generalization of the classic Kuga-Satake construction (joint with M.Verbitsky and A.Soldatenkov) which allows us to embed cohomology of hyperkähler manifolds to cohomology of some complex torus, and it is a morphism of Hodge structures . Also I will briefly explain some interesting corollaries.