Kuga-Satake construction and cohomology of hyperkahler manifolds

Mardi 4 décembre 2018 14:15-15:15 - Misha Verbitsky - IMPA

Résumé : Let M be a maximal holonomy hyperkahler manifold. Kuga-Satake
construction gives an embedding of H^2(M,C) into the second cohomology of
a torus, compatible with the Hodge structure. We construct a torus T and an
embedding of the total cohomology space H^*(M,C) into H^*+1(T,C) for
some l, which is compatible with the Hodge structures and the Poincare pairing.
Moreover, this embedding is compatible with an action of the Lie algebra
generated by all Lefschetz sl(2)-triples on M. This is a joint work with
Nikon Kurnosov and Andrey Soldatenkov. Our research was motivated
by trying to construct a higher-dimensional analogue of the Beauville-Bogomolov-Fujiki form.

Kuga-Satake construction and cohomology of hyperkahler manifolds  Version PDF