Freeness for multiarrangements of hyperplanes over arbitrary fields

TL;DR

This paper explores the conditions under which multiarrangements of hyperplanes are free over different fields, analyzing the relationship between freeness in finite characteristic fields and over the rationals.

Contribution

It establishes new connections between freeness properties of hyperplane arrangements over various fields, extending understanding beyond characteristic zero.

Findings

Freeness over finite fields can differ from that over rationals.

Identifies conditions linking freeness over different fields.

Provides criteria for freeness in multiarrangements.

Abstract

In this paper, we study the class of free multiarrangements of hyperplanes. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over the rationals.