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Generalized polygons with non-discrete valuation defined by two-dimensional affine ℝ-buildings
-
Koen Struyve
Veröffentlicht/Copyright:
8. Juli 2010
Abstract
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 
, and it reproves the results obtained mainly by the second author for types 
and 
. 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).
Received: 2008-03-06
Revised: 2008-04-30
Published Online: 2010-07-08
Published in Print: 2010-July
© de Gruyter 2010
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Artikel in diesem Heft
- On the characteristic direction of real hypersurfaces in and a symmetry result
- Small maximal partial spreads in classical finite polar spaces
- On antipodes on a convex polyhedron II
- On the quadratic normality and the triple curve of three-dimensional subvarieties of
- A generalization of the Giulietti–Korchmáros maximal curve
- Busemann Functions and the Julia–Wolff–Carathéodory Theorem for polydiscs
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- Measures on the space of convex bodies
- On the scalar curvature of hypersurfaces in spaces with a Killing field
- The real quadrangle of type E6
- Triple-point defective surfaces
- On surfaces with pg = 2q – 3
- A counter example to an ideal membership test
