Singular spaces with trivial canonical class

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• Daniel Greb (Freiburg)
• Monday 10 October 2011, 15:00-16:00
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

The Beauville-Bogomolov decomposition theorem asserts that any compact Kahler 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 etale 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, we prove 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.

This talk is part of the Algebraic Geometry Seminar series.

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