Algebraic Geometry Seminar

Kuga-Satake construction and cohomology of hyperkahler manifolds

Speaker: Nikon Kurnosov, HSE, Moscow

Location: Warren Weaver Hall 605

Date: Friday, October 27, 2017, 2 p.m.


I will talk about our recent work with A.Soldatenkov and M.Verbitsky. We show that all cohomology of hyperkahler manifold X
can be embedded into the cohomology of the product of several copies of abelian variety A. This is the generalization of classical Kuga-Satake construction, which attaches to the rational polarized weight 2 Hodge structure of K3 type H
an abelian variety A and an embedding of H into the second cohomology of A, compatible with Hodge structures.