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SFB-Seminartag in Bonn

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Duco von Straten (Mainz) and Daniel Greb (Essen)

  • SFB-Kolloquium
When Dec 03, 2015
from 02:15 pm to 05:45 pm
Where Bonn, Lipschitzsaal (1.016)
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14:15 Duco Van Straten: Calabi-Yau Periods

15:45 Coffee and cake

16:30 Daniel Greb: Higher-dimensional Birational Geometry - Minimal Model Program, Miyaoka-Yau Inequality, and Uniformisation

 After an introduction to the basic goals and notions of higher-dimensional birational geometry and the minimal model program, I will concentrate on the case of varieties of general type. By the seminal work of Birkar-Cascini-Hacon-McKernan (~2006) the minimal model program is known to work for these, so that every smooth projective variety of general type admits a minimal as well as a canonical model. Motivated by Riemann's Uniformisation Theorem in one complex variable, I will then describe approaches to higher-dimensional uniformisation theorems. Time permitting, at the end of my talk I will explain the proof of a recent result (with Kebekus, Peternell, and Taji) that establishes the Miyaoka-Yau Inequality (MYI) for minimal varieties of general type and characterises those varieties for which the MYI becomes an equality as quotients of the unit ball by a cocompact discrete subgroup of PSU(n-1,1).