A Second Main Theorem for Moving Hypersurface Targets

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.

37 pages. to appear in Houston J. Math

Cited by in corpus (7)

• An explicit estimate on multiplicity truncation in the second main theorem for holomorphic curves encountering hypersurfaces in general position in projective space
• Meromorphic mappings into projective varieties with arbitrary families of moving hypersurfaces
• Schmidt's subspace theorem for moving hypersurface targets
• Second main theorem for meromorphic mappings with moving hypersurfaces in subgeneral position
• Second main theorem for holomorphic curves into algebraic varieties intersecting moving hypersurfaces targets
• Holomorphic maps from complex discs intersecting families of hypersurfaces
• An Extension of the Cartan-Nochka Second Main Theorem for Hypersurfaces