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On holomorphic foliations admitting invariant CR manifolds (1910.01930v2)
Published 3 Oct 2019 in math.CV, math.AG, math.DG, and math.DS
Abstract: We study holomorphic foliations of codimension $k\geq 1$ on a complex manifold $X$ of dimension $n+k$ from the point of view of the exceptional minimal set conjecture. For $n\geq 2$ we show in particular that if the holomorphic normal bundle $N_{\mathcal{F}}$ is Griffiths positive, then the foliation does not admit a compact invariant set that is a complete intersection of $k$ smooth real hypersurfaces in $X$.