Holomorphic symplectic manifolds: IHS vs BG-manifolds

Nikon Kurnosov, University College London

I will discuss examples of irreducible holomorphic symplectic manifolds, which are essentially hyperkahler in a Kahler case. However, without the Kahler assumption holomorphically symplectic manifolds are not necessarily hyperkahler. Higher-dimensional simply-connected non-Kahler holomorphically symplectic manifolds have been constructed by Guan and by Bogomolov. I will talk about the differences and similiarities in the geometry of hyperkahler and BG-manifolds and about ideas which can lead to the proof of the finiteness of the deformation types in any dimension.

MC 5417

Note special time for this talk.