Algebraic Geometry Seminar
Behrouz TAJI
Northwestern University.
The Miyaoka-Yau inequality for minimal models of general type and uniformization.
Abstract: By proving Calabi's conjecture, Yau proved that the Chern classes of a compact manifold with
ample canonical bundle encode the symmetries of the Kahler-Einstein metric via a simple inequality
-- the so-called Miyaoka-Yau inequality. Furthermore it was shown that in the case of equality, the
universal cover is the ball. Later, Tsuji established the MY inequality for smooth minimal models of general
type by constructing singular Kahler-Einstein metrics. The singularity of these metrics are usually a major
obstacle towards uniformization; a problem that has not yet been resolved via analytic methods. In a joint
project with Greb, Kebekus and Peternell, we take a different approach, via Hermitian-Yang-Mills theory and
Simpson's groundbreaking work on complex variation of Hodge structures, and we prove the MY inequality
for minimal models of general type and establish a uniformization result for their canonical models.
Wednesday October 12, 2016 at 4:00 PM in SEO 427