The Dimensions of Integral Points and Holomorphic Curves on the Complements of Hyperplanes
Number Theory
2007-05-23 v1 Complex Variables
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.
Cite
@article{arxiv.math/0601691,
title = {The Dimensions of Integral Points and Holomorphic Curves on the Complements of Hyperplanes},
author = {Aaron Levin},
journal= {arXiv preprint arXiv:math/0601691},
year = {2007}
}
Comments
10 pages