Degeneracy of holomorphic curves in surfaces

作     者：LIU Yuancheng RU Min 

作者机构：Department of MathematicsUniversity of HoustonHoustonTX 77204USA Department of MathematicsUniversity of HoustonHoustonTX 77204USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2005年第48卷第z1期

页      面：156-167页

核心收录：

学科分类：07[理学] 08[工学] 

基　　金：National Security Agency  NSA  (MSPF-02G-175) 

主　　题：degeneracy of holomorphic curves, Nevanlinna theory, complex projective surface, second main theorem. 

摘      要：Let X be a complex projective algebraic manifold of dimension 2 and let D1,..., Du be distinct irreducible divisors on X such that no three of them share a common point. Let f: C → X\(U1≤i≤uDi) be a holomorphic map. Assume that u ≥ 4 and that there exist positive integers n1,...,nu, c such that ninj(***) = c for all pairs i, j. Then f is algebraically degenerate, i.e. its image is contained in an algebraic curve on X.