A Representation Theorem for Generic Line Arrangements with Global Cyclicity in the Plane

TL;DR

This paper proves a representation theorem showing that any generic line arrangement with global cyclicity in the plane can be isomorphically represented by an arrangement with specified slopes, linking geometric structure to slope configurations.

Contribution

It introduces a representation theorem connecting global cyclicity in line arrangements to arrangements with prescribed slopes over an ordered field.

Findings

Any generic line arrangement with global cyclicity can be represented with a fixed set of slopes.

The theorem applies to arrangements over an ordered field.

Provides a structural understanding of cyclic arrangements in the plane.

Abstract

In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes of the same cardinality.