On triples of ideal chambers in A2-buildings

TL;DR

This paper explores the geometric configurations of ideal chambers in A2-buildings, linking them with projective invariants like the cross ratio and classifying generic triples based on the triple ratio of flags.

Contribution

It provides a geometric classification of generic triples of ideal chambers in A2-buildings and relates these configurations to projective invariants such as the triple ratio.

Findings

Classified generic triples of ideal chambers in A2-buildings.

Connected geometric configurations with projective invariants.

Established relations between chamber configurations and the triple ratio.

Abstract

We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of generic triples of ideal chambers of X and relate it with the triple ratio of triples of flags.