The MiyaokaYau inequality for minimal models of general type and the uniformization by the ball
Behrouz Taji (Freiburg)  Seminar Algebraic Geometry (SAG)
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When 
Nov 12, 2015 from 10:30 pm to 11:30 pm 
Where  Bonn, HĂ¶rsaal MPI, Vivatsgasse 7 
Contact Name  Sachinidis 
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By proving Calabi's conjecture, Yau proved that the first and second Chern classes of a compact manifold with ample canonical bundle encode the symmetries of the KahlerEinstein metric via a simple inequality ; the socalled Miyaoka Yau inequality. In the case of equality, such symmetries lead to the uniformization by the ball. Later, by constructing singular KE metrics, Tsuji established this inequality for smooth minimal models of general type. The singularity of these metrics are usually a major obstacle towards uniformization. In a joint project with Greb, Kebekus and Peternell we take a different approach; using HermitianYangMills theory and Simpson's groundbreaking work on complex variation of Hodge structures, we prove the MY inequality for minimal models of general type and show that when the equality holds, the canonical models are ballquotients.