Local Sharply Transitive Actions on Finite Generalized Quadrangles

2011 ◽  
Vol 15 (1) ◽  
pp. 69-80
Author(s):  
Theo Grundhöfer ◽  
Hendrik Van Maldeghem
Keyword(s):  
Generalized Quadrangles ◽  
Transitive Actions ◽  
Sharply Transitive

scholarly journals Geometrically rational real conic bundles and very transitive actions

2010 ◽  
Vol 147 (1) ◽  
pp. 161-187 ◽  
Author(s):  
Jérémy Blanc ◽  
Frédéric Mangolte
Keyword(s):  
Automorphism Groups ◽  
Algebraic Surfaces ◽  
Algebraic Models ◽  
Transitive Automorphism ◽  
Real Locus ◽  
Real Algebraic Surfaces ◽  
Conic Bundles ◽  
Transitive Actions ◽  
Insight Into

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

scholarly journals MOUFANG QUADRANGLES OF MIXED TYPE

2008 ◽  
Vol 50 (1) ◽  
pp. 143-161
Author(s):  
KOEN STRUYVE ◽  
HENDRIK VAN MALDEGHEM
Keyword(s):  
Mixed Type ◽  
Geometric Characterization ◽  
Weak Version ◽  
Generalized Quadrangles

AbstractIn this paper, we present some geometric characterizations of the Moufang quadrangles of mixed type, i.e., the Moufang quadrangles all the points and lines of which are regular. Roughly, we classify generalized quadrangles with enough (to be made precise) regular points and lines with the property that the dual nets associated to the regular points satisfy the Axiom of Veblen-Young, or a very weak version of the Axiom of Desargues. As an application we obtain a geometric characterization and axiomatization of the generalized inversive planes arising from the Suzuki-Tits ovoids related to a polarity in a mixed quadrangle. In the perfect case this gives rise to a characterization with one axiom less than in a previous result by the second author.

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