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Algebraic integrability of foliations with numerically trivial canonical bundle. (English) Zbl 07061101
Summary: 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.

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
37F75 Dynamical aspects of holomorphic foliations and vector fields
14E30 Minimal model program (Mori theory, extremal rays)
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