Year: 2007
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Dethloff, Gerd, Van Tan, Tran
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1542443981