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# Singular spaces with trivial canonical class

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Daniel Greb (U Freiburg, z.Z. MI Bonn)

What Seminar May 03, 2012 from 10:30 am to 11:30 am Bonn Hörsaal MPI, Vivatsgasse 7 Sachinidis vCal iCal

The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with trivial canonical bundle is finitely covered by the product of a compact complex torus, simply connected Calabi-Yau manifolds, and simply connected irreducible holomorphic symplectic manifolds. The decomposition of the étale cover corresponds to a decomposition of the tangent bundle into a direct sum, whose summands are integrable and stable with respect to any polarization. Building on recent extension theorems for differential forms on singular spaces, in the talk I will sketch the proof of an analogous decomposition theorem for the tangent sheaf of a projective variety with canonical singularities and numerically trivial canonical class. This is joint work with Stefan Kebekus and Thomas Peternell.