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Acta Mathematica Vietnamica

Second Main Theorem and Unicity of Meromorphic Mappings for Hypersurfaces in Projective Varieties

icon-email Si Duc Quang , Do Phuong An

Abstract

Let V be a projective subvariety of Pn(C). A family of hypersurfaces {Qi}i=1q in Pn(C) is said to be in N-subgeneral position with respect to V if for any 1i1<<iN+1q, V(j=1N+1Qij)=. In this paper, we will prove a second main theorem for meromorphic mappings of Cm into V intersecting hypersurfaces in subgeneral position with truncated counting functions. As an application of the above theorem, we give a uniqueness theorem for meromorphic mappings of Cm into V sharing a few hypersurfaces without counting multiplicity. In particular, we extend the uniqueness theorem for linearly nondegenerate meromorphic mappings of Cm into Pn(C) sharing 2n+3 hyperplanes in general position to the case where the mappings may be linearly degenerated.