vix.ing · top · new · best · stats · spec

The Dimensions of Integral Points and Holomorphic Curves on the Complements of Hyperplanes

2006/01/27 by Aaron Levin, Levin, Aaron
Mathematics · #11D57 #11D72 #32H30 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.CV #math.NT #msc:11D57 #msc:11D72 #msc:32H30

paper · pdf · doi:10.48550/arxiv.math/0601691

10 pages

arxiv created 2006/01/27 · openalex publication_date 2006/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we completely determine the possible dimensions of integral points and holomorphic curves on the complement of a union of hyperplanes in projective space. Our main theorems generalize a result of Evertse and Gyory, who determined when all sets of integral points (over all number fields) on the complement of a union of hyperplanes are finite, and a result of Ru, who determined when all holomorphic maps to the complement of a union of hyperplanes are constant. The main tools used are the S-unit lemma and its analytic analogue, Borel's lemma.

Citations

Related