Tits arrangements on cubic curves

TL;DR

This paper classifies specific affine rank three Tits arrangements on cubic curves, revealing the existence of irreducible arrangements that are not locally spherical, expanding understanding of geometric configurations.

Contribution

It provides a classification of affine rank three Tits arrangements on cubic curves and identifies new arrangements that are not locally spherical.

Findings

Existence of irreducible affine Tits arrangements not locally spherical

Complete classification of arrangements with roots on cubic curves

New geometric configurations identified

Abstract

We classify affine rank three Tits arrangements whose roots are contained in the locus of a homogeneous cubic polynomial. We find that there exist irreducible affine Tits arrangements which are not locally spherical.