Singular spaces with trivial canonical class
Stefan Kebekus (Freiburg)
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When 
Jul 12, 2012 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract: The classical BeauvilleBogomolov 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, simplyconnected CalabiYau? and holomorphicsymplectic manifolds. The decomposition of the simplyconnected 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 CalabiYau? and irreducible holomorphicsymplectic manifolds, respectively.