Abstract

By introducing the notion of distributive constant of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary families of hypersurfaces. Our second main theorem generalizes and improves previous results for meromorphic mappings with hypersurfaces, in particular for algebraically nondegenerate mappings with hypersurfaces in subgeneral position. The analogous results for the holomorphic curves with finite growth index from a complex disc into a projective variety, and for meromorphic mappings on a complete Kähler manifold are also given. For the last aim, we will prove a Schmidt’s subspace theorem for arbitrary families of homogeneous polynomials, which is the counterpart in the number theory of our second main theorem.

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