A Second Main Theorem for Moving Hypersurface Targets

Details A Second Main Theorem for Moving Hypersurface Targets A Second Main Theorem for Moving Hypersurface Targets

2007-03-20

arxiv.org/abs/math/0703572v2

Mathematics

Complex Variables

37 pages. to appear in Houston J. Math

Scientific paper

In 1979, B. Shiffman conjectured that if f is an algebraically nondegenerate holomorphic map of C into P^n and D_1,...,D_q are hypersurfaces in P^n 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.

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