Algebraic integrability of foliations with numerically trivial canonical bundle

By A. Höring, T. Peternell. Inventiones Mathematicae, 2017

111 citations recorded by the source corpus.

Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second Chern class does not vanish. Combined with the recent works of Druel and Greb–Guenancia–Kebekus this establishes the Beauville–Bogomolov decomposition for minimal models with trivial canonical class.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b0d4419a988273e333c4b389a3b951b7d078998a

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In Geometry and Topology

1. Stefan Kebekus
2. D. Greb
3. Henri Guenancia
4. T. Peternell
5. S. Druel
6. Carolina Araujo
7. Yanir A. Rubinstein
8. Robert J. Berman

In Statistical and Nonlinear Physics

1. Stefan Kebekus
2. Henri Guenancia
3. D. Greb

Citations in the corpus

• Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups (2017, methodology): “Using Druel’s strategy as well as the results presented in this paper, in particular Proposition D and Theorem E below, Höring and Peternell very recently gave a proof of the singular version of the Decomposition Theorem in [HP17], thus completing the long quest for such a result in the singular cat”