Deformation Classification of Typical Configurations of 7 Points in the Real Projective Plane

TL;DR

This paper classifies the deformation types of typical 7-point configurations in the real projective plane, providing a comprehensive understanding of their geometric arrangements and linking to real Aronhold sets.

Contribution

It introduces a complete classification of 14 deformation classes for typical 7-point configurations in RP2, connecting geometric configurations to Aronhold sets.

Findings

14 deformation classes of typical 7-point configurations identified

Classification of real Aronhold sets achieved

No collinear triples or coconic sextuples in classified configurations

Abstract

A configuration of 7 points in RP2 is called typical if it has no collinear triples and no coconic sextuples of points. We show that there exist 14 deformation classes of such configurations. This yields classification of real Aronhold sets.