Seminar in Real and Complex Geometry
Tuesday, 21.07.2015, 16:00-17:00,
Schreiber
building, room 209
Mikhail Verbitsky,
High School of Economics
Proof of Morrison-Kawamata cone conjecture for hyperkahler manifolds
Abstract
Morrison-Kawamata cone conjecture is a conjecture
about the shape of an ample cone of a Calabi-Yau manifold.
Morrison and Kawamata predicted that it is a
polyhedron and the automorphism group acts on its
faces with finitely many orbits. For hyperkahler
manifolds it is proven; the proof is based on
a result of hyperbolic geometry which is deduced
from the Ratner theory of ergodic action on
homogeneous spaces. I will tell the general scheme
of the proof and explain how Ratner theory fits
into the picture. This is a joint work with
Ekaterina Amerik.
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