Abstract. The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of hypersurfaces in subgeneral position. In our result, the truncation level of the counting functions is estimated explicitly. Our result is an extension of the classical second main theorem of H. Cartan, also is a generalization of the recent second main theorem of M. Ru and improves some recent results. The second purpose of this paper is to give another proof for the second main theorem for the special case where the projective variety is a projective space, by which the truncation level of the counting functions is estimated better than that of the general case.

The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of C m into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions. The second is to show a uniqueness theorem for these mappings which share few hypersurfaces without counting multiplicity.

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