On holomorphic foliations admitting invariant CR manifolds

Judith Brinkschulte

On holomorphic foliations admitting invariant CR manifolds

Complex Variables 2021-07-07 v2 Algebraic Geometry Differential Geometry Dynamical Systems

Authors: Judith Brinkschulte

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 $X$ .

Keywords

holomorphic foliations invariant cr manifolds exceptional minimal set griffiths positive complex manifold

Cite

@article{arxiv.1910.01930,
  title  = {On holomorphic foliations admitting invariant CR manifolds},
  author = {Judith Brinkschulte},
  journal= {arXiv preprint arXiv:1910.01930},
  year   = {2021}
}

Comments

to be published in Ann. Sc. Norm. Sup. Pisa. arXiv admin note: text overlap with arXiv:1804.06884

On holomorphic foliations admitting invariant CR manifolds

Abstract

Keywords

Cite

Comments

Related papers