Christian Lehn

Christian Lehn (Chemnitz University of Technology) visited Laboratory of Algebraic Geometry in December 2019 at the invitation of research fellow Nikon Kurnosov.

On December 9th 2019 he gave a talk A new proof of the Global Torelli Theorem for holomorphic symplectic varieties at the seminar of Laboratory.
Abstract: In a joint work with Benjamin Bakker, we develop a theoretical framework to approach the global moduli theory of certain singular symplectic varieties. Our work is based on new results about the deformation theory of these varieties together with the notion of ergodic complex structures which has been introduced by Verbitsky and used to study for example hyperbolicity questions. I will explain how to use these techniques to prove a Global Torelli theorem for the varieties in question. Our result in particular gives a new proof of Verbitsky's Global Torelli Theorem for irreducible symplectic manifolds as soon as the second Betti number is at least 5