Singular spaces with trivial canonical class

Details Singular spaces with trivial canonical class Singular spaces with trivial canonical class

2011-10-24

arxiv.org/abs/1110.5250v2

Mathematics

Algebraic Geometry

30 pages. Version 2 streamlines the argumentation and fixes a minor issue in Section 4

Scientific paper

The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact K\"ahler manifold with numerically trivial canonical bundle admits an \'etale 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.

Affiliated with

Also associated with

No associations

Rating

Singular spaces with trivial canonical class does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singular spaces with trivial canonical class, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular spaces with trivial canonical class will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-520743