A Second Main Theorem for Moving Hypersurface Targets

الأصل · EN

In 1979, B. Shiffman conjectured that if f is an algebraically nondegenerate holomorphic map of C into Pⁿ and D₁,...,Dq are hypersurfaces in Pⁿ in general position, then the sum of the defects is at most n+1. This conjecture was proved by M. Ru in 2004. In this paper, the Shiffman conjecture is proved more generally in the case of slowly moving hypersurfaces in (weakly) general position. Moreover, we introduce a truncation in the corresponding Second Main Theorem, with an effective estimate on the truncation level, thus generalizing a result of An-Phuong.