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Global stability for holomorphic foliations on Kähler manifolds. (English) Zbl 1074.53019
The author proves the global stability theorem for holomorphic foliations:
Theorem 1. Let $$\mathcal{F}$$ be a holomorphic foliation of codimension $$q$$ on a compact complex Kähler manifold. If $$\mathcal{F}$$ has a compact leaf with finite holonomy group then every leaf of $$\mathcal{F}$$ is compact with finite holonomy group.
This theorem allows the author to reobtain H. Holmann’s [Lect. Notes Math. 798, 192–202 (1980; Zbl 0451.57014)] result and a special case of Edwards-Millet-Sullivan’s theorem [R. Edwards, K. Millett and D. Sullivan, Topology 16, 13–32 (1977; Zbl 0356.57022)].

##### MSC:
 53C12 Foliations (differential geometric aspects) 57R30 Foliations in differential topology; geometric theory
##### Keywords:
holomorphic foliation; holonomy; compact leaf
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##### References:
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