Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Christian Lehn
Affiliation:

Chemnitz Universität
Date:

Wed, 2017-11-29 10:30 - 11:30 Verbitsky's global Torelli theorem has been one of the most important advances in the theory of holomorphic

symplectic manifolds in the last years. In a joint work with Ben Bakker (University of Georgia) we prove a

version of the global Torelli theorem for singular symplectic varieties and discuss applications. Symplectic

varieties have interesting geometric as well as arithmetic properties, their birational geometry is particularly

rich. We focus on birational contractions of symplectic varieties and generalize a number of known results

for moduli spaces of sheaves to general deformations.

Our results are obtained through the interplay of Hodge theory, deformation theory, and a further example

of Verbitsky's technique which might carry the name "how to deduce beautiful consequences from ugly

behavior of moduli spaces''.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/YRSM2017