Universal covers of higher dimensional singular spaces

Behrouz Taji

http://home.mathematik.uni-freiburg.de/taji/

Date(s) : 01/02/2016   iCal
14 h 00 min - 15 h 00 min

By proving Calabi’s conjecture, Yau proved that the first and second Chern classes of a compact complex manifold with ample canonical bundle encode the symmetries of the Kahler-Einstein metric via a simple inequality; the so-called Miyaoka-Yau inequality. In the case of equality, such symmetries lead to the uniformization by the ball. In the classification theory of complex varieties, one looks at a far bigger class of varieties than those with ample canonical bundle, but still comparable. These are referred to as minimal models of general type, and their existence has been one of the most important recent breakthroughs in the classification theory. Unfortunately, for these varieties many of the analytic tools of (smooth) Kahler-Eistein theory falls apart. In a joint work with Greb, Kebekus and Peternell we remedy this by exploiting Hodge theoretic methods developed by Simpson, and extend Yau’s result to the class of minimal models of general type.

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