Free hyperplane arrangements over arbitrary fields

TL;DR

This paper explores the properties of free hyperplane arrangements over various fields, examining how freeness in finite characteristic fields relates to freeness over the rational numbers.

Contribution

It provides new insights into the relationship between freeness over finite characteristic fields and over the rationals for hyperplane arrangements.

Findings

Freeness over finite characteristic fields can differ from freeness over .

Conditions under which freeness over  implies freeness over finite fields.

New criteria for determining freeness in different field characteristics.

Abstract

In this paper, we study the class of free hyperplane arrangements. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over $\mathbb{Q}$.