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Regular version of the site

Book chapter

Teichmuller spaces, ergodic theory and global Torelli theorem

P. 793-811.

A Teichmüller space Teich is a quotient of the space of all complex structures on a given
manifoldM by the connected components of the group of diffeomorphisms. The mapping class group
Γ ofM is the group of connected components of the diffeomorphism group. The moduli problems can
be understood as statements about the Γ-action on Teich. I will describe the mapping class group and
the Teichmüller space for a hyperkähler manifold. It turns out that this action is ergodic. We use the
ergodicity to show that a hyperkähler manifold is never Kobayashi hyperbolic.






In book

Vol. 2. Seul: Kyung Moon Sa Co. Ltd, 2014.