1996/10/14 by Yum-Tong Siu, Siu, Yum-Tong, Sai-Kee Yeung +1
Mathematics · #32 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.math/9610203
openalex publication_date 1996/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of this paper is to prove the following theorem on the defect relations for ample divisors of abelian varieties. Main Theorem. Let A be an abelian variety of complex dimension n and D be an ample divisor in A. Let f:\bf C→ A be a holomorphic map. Then the defect for the map f and the divisor D is zero. Corollary to Main Theorem. The complement of an ample divisor D in an abelian variety A is hyperbolic in the sense that there is no nonconstant holomorphic map from \bf C to A-D.