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Finite Cn geometries: a survey

Finite \(C_ n\) geometries: A survey
Authors: LUNARDON, GUGLIELMO; A. Pasini;

Finite Cn geometries: a survey

Abstract

This paper is an excellent survey of about everything what is known concerning the classification of residual connected Buekenhout-Tits geometries with Buekenhout diagram \(C_ n\). A complete classification of such geometries is hopeless, but with some additional hypotheses, large subclasses can be classified. The additional hypotheses considered in the paper under review are combinations of: being ordinary (= all lines are thick), flat (= all hyperlines are incident with all elements not being hyperlines nor hyperplanes), degenerate (= non-ordinary), thick, thin; admitting parameters of known type, classical type, semi-classical type; being locally classical, finite, infinite; admitting a flag-transitive automorphism group. The paper is roughly divided in two pieces: one part (section 1) describes the known results and states the theorems, giving useful comments and conjectures to let the reader feel where the theory is coming from and where the research is going to. In the second part (sections 2, 3, 4, 5), sketches of the proofs are given. The authors have tried to unify the theory and consequently they were able to simplify existing proofs. Also background information is not avoided, e.g., results on flag-transitive projective planes and generalized quadrangles is given in full generality. Well, I have enjoyed this paper, why wouldn't you?

Country
Italy
Keywords

Research exposition (monographs, survey articles) pertaining to geometry, Buildings and the geometry of diagrams, survey, classification of residual connected Buekenhout-Tits geometries, buildings, Buekenhout diagram

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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