Personal tools
You are here: Home Events Singular spaces with trivial canonical class

Singular spaces with trivial canonical class

— filed under:

Stefan Kebekus (Freiburg)

What
  • SFB-Kolloquium
When Jul 12, 2012
from 03:15 pm to 04:15 pm
Where Mainz, 05-432 (Hilbertraum)
Add event to calendar vCal
iCal
 
 
 

Abstract: The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, and irreducible, simply-connected Calabi-Yau? and holomorphic-symplectic manifolds. The decomposition of the simply-connected part corresponds to a decomposition of the tangent bundle into a direct sum whose summands are integrable and stable with respect to any polarisation. Building on recent extension theorems for differential forms on singular spaces, we prove an analogous decomposition theorem for the tangent sheaf of projective varieties with canonical singularities and numerically trivial canonical class.

 

In view of recent progress in minimal model theory, this result can be seen as a first step towards a structure theory of manifolds with Kodaira dimension zero. Based on our main result, we argue that the natural building blocks for any structure theory are two classes of canonical varieties, which generalise the notions of irreducible Calabi-Yau? and irreducible holomorphic-symplectic manifolds, respectively.

 

 

May 2018 »
May
MoTuWeThFrSaSu
123456
78910111213
14151617181920
21222324252627
28293031