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PIRSA:19100056

Video URL

https://pirsa.org/19100056

Cohomology of hyperkahler manifolds

Kurnosov, N. (2019). Cohomology of hyperkahler manifolds. Perimeter Institute for Theoretical Physics. https://pirsa.org/19100056

Nikon Kurnosov University of Georgia

Talk numberPIRSA:19100056
DOI10.48660/19100056
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

I will talk about compact hyperkahler manifolds, which generalize the famous K3 surface to the higher dimensions. Given a compact simple hyperkahler manifold $M$, I will describe how the structure of cohomology algebra H*(M) is related with the so(b_2+2) Lie algebra action and the second cohomology group. I will explain how this is applied to the generalization of Kuga-Satake construction which allows us to assign for K3-type Hodge structure a Hodge structure of weight one (i.e. complex torus).