We will prove the holomorphic Reeb stability theorem [3, Thm 2.4 and 2.5]. This structural theorem for algebraic foliations explains why the definition of algebraicity in [2, Def 4.1] and in [1, Def 3.1] are equivalent.

 

Ref. 

[1] Stéphane Druel. A decomposition theorem for singular spaces with trivial canonical class of dimension at most five. Invent. Math., 211(1):245–296, 2018. 

[2] Frédéric Campana and Mihai Paun, Foliations with positive slopes and birational stability of orbifold cotangent bundles. Publ. Math. Inst. Hautes Études Sci., 129:1–49, 2019.

[3] Jun-Muk Hwang and Eckart Viehweg. Characteristic foliation on a hypersurface of general type in a projective symplectic manifold. Compos. Math., 146(2):497–506, 2010.