# An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory

## TL;DR

This paper improves the point-line incidence bounds over finite fields by applying VC-dimension theory, leading to enhanced results in combinatorial geometry with various applications.

## Contribution

It introduces a novel approach using VC-dimension theory to refine existing incidence bounds over finite fields.

## Key findings

- Improved incidence bounds in specific finite field ranges
- Enhanced combinatorial geometry results
- New applications derived from the improved bounds

## Abstract

The main purpose of this paper is to prove that the point-line incidence bound due to Vinh (2011) over arbitrary finite fields can be improved in certain ranges by using tools from the VC-dimension theory. As consequences, a number of applications will be discussed in detail.