Vol. 17, No. 2, 2019

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On triples of ideal chambers in $A_2$-buildings

Anne Parreau

Vol. 17 (2019), No. 2, 109–140
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 , seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on ). 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.

Keywords
Euclidean buildings, projective planes, ideal configurations, triple ratio
Mathematical Subject Classification 2010
Primary: 51E24
Secondary: 20E42
Milestones
Received: 21 July 2016
Revised: 10 December 2018
Accepted: 29 December 2018
Published: 31 May 2019
Authors
Anne Parreau
Université Grenoble Alpes
CNRS
IF
Grenoble
France