Bounds on leaves one-dimensional foliations.

Let X be a variety over an algebraically closed field, η: Ω[sup 1, sub X] → L a one-dimensional singular foliation, and C ⊆ X a projective leaf of η. We prove that 2p[sub a](C) - 2 = deg(LC) + λ(C) - deg(C ∩ S) where p[sub a] (C) is the arithmetic genus, where λ(C) is the co-length in the dualizing sheaf of the subsheaf generated by the Kähler differentials, and where S is the singular locus of η. We bound λ(C) and deg(C ∩ S), and then improve and extend some recent results of Campillo, Carnicer, and de la Fuente, and of du Plessis and Wall. [ABSTRACT FROM AUTHOR]