PIRSA:19100056

Cohomology of hyperkahler manifolds

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

Kurnosov, Nikon. Cohomology of hyperkahler manifolds. Perimeter Institute, Oct. 03, 2019, https://pirsa.org/19100056 

          @misc{ pirsa_PIRSA:19100056,
            doi = {10.48660/19100056},
            url = {https://pirsa.org/19100056},
            author = {Kurnosov, Nikon},
            keywords = {Mathematical physics},
            language = {en},
            title = {Cohomology of hyperkahler manifolds},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {oct},
            note = {PIRSA:19100056 see, \url{https://pirsa.org}}
          }

Nikon Kurnosov

University of Georgia

Talk number
PIRSA:19100056
Collection
Talk Type
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).