2009/09/27 by Koen Struyve, Hendrik Van Maldeghem, Struyve, Koen +1
Computer Science · Mathematics · #51E24 #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.0909.4962
openalex publication_date 2009/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that the building at infinity of a two-dimensional affine R-building is a generalized polygon endowed with a valuation satisfying some specific axioms. Specializing to the discrete case of affine buildings, this solves part of a long standing conjecture about affine buildings of type G~2, and it reproves the results obtained mainly by the second author for types A~2 and C~2. The techniques are completely different from the ones employed in the discrete case, but they are considerably shorter, and general (i.e., independent of the type of the two-dimensional R-building).