an:02161123
Zbl 1074.53019
Pereira, J. V.
Global stability for holomorphic foliations on K??hler manifolds
EN
Qual. Theory Dyn. Syst. 2, No. 2, 381-384 (2002).
00079443
2002
j
53C12 57R30
holomorphic foliation; holonomy; compact leaf
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 K??hler 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 \textit{H. Holmann}'s [Lect. Notes Math. 798, 192--202 (1980; Zbl 0451.57014)] result and a special case of Edwards-Millet-Sullivan's theorem [\textit{R. Edwards, K. Millett} and \textit{D. Sullivan}, Topology 16, 13--32 (1977; Zbl 0356.57022)].
Vladimir Yu. Rovenskij (Nesher)
Zbl 0451.57014; Zbl 0356.57022