Séminaire Géométries ICJ

Generalized Kuga-Satake construction for hyperkähler manifolds

by Nikon Kurnosov

112 (ICJ)



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

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.

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