The Second Main Theorem with moving hypersurfaces in subgeneral position

2025/01/01 by Qili Cai, Cai, Qili, Chin-Jui Yang +1
Mathematics · #32A22 (Secondary) #32H30 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2501.00833

openalex publication_date 2025/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a second main theorem for a holomorphic curve f into \mathbb P^N (\mathbb C) with a family of slowly moving hypersurfaces D₁,...,D_q with respect to f in m-subgeneral position, proving an inequality with factor 3 \over 2. The motivation comes from the recent result of Heier and Levin.

Related

• Cartan's Conjecture for Moving Hypersurfaces
• A Non-Archimedean Second Main Theorem for Hypersurfaces in Subgeneral Position
• Holomorphic Curves into Algebraic Varieties Intersecting Divisors in Subgeneral Position
• Holomorphic curves into algebraic varieties intersecting moving hypersurface targets
• An explicit estimate on multiplicity truncation in the second main theorem for holomorphic curves encountering hypersurfaces in general position in projective space