Algebraic degeneracy of holomorphic curves

2021/03/17 by Xianjing Dong, Dong, Xianjing, Pei-Chu Hu +1
Mathematics · #30D35 #32H30 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2103.09611

openalex publication_date 2021/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the algebraic degeneracy of holomorphic curves from a point of view of meromorphic vector fields. Employing the notion of Jocabian sections introduced by W. Stoll, we establish a Second Main Theorem type inequality. As consequences, several algebraic degeneracy theorems are obtained for holomorphic curves into a complex projective variety.

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