Bounds on Leaves of One-dimensional Foliations
نویسنده
چکیده
Let X be a variety over an algebraically closed field, η : Ω X → Ļ a onedimensional singular foliation, and C ⊆ X a projective leaf of η. We prove that 2pa(C)−2 = deg(Ļ|C)+λ(C)−deg(C∩S) where pa(C) is the arithmetic genus, where λ(C) is the colength 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.
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تاریخ انتشار 2002