Algebraic Geometry Seminar
Rigid currents on hyperkahler manifolds.
Speaker: Misha Verbitsky
Location: Warren Weaver Hall 317
Date: Friday, January 25, 2019, 3:30 p.m.
A positive current is a positive (p,p)-form with
coefficients in measures. It is not hard to show that
any cohomology class on the boundary of a Kahler cone
can be represented by a closed, positive current.
This class is called rigid if its representative
current is unique. Any Kahler class on the
boundary of the Kahler cone of a hyperkahler
manifold is rigid, if it is irrational and
has zero volume. I would explain how this
result is proven, using ergodic theory. This
is a joint work with Nessim Sibony.