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A COMBINATORIAL CHARACTERIZATION OF THE LAGRANGIAN GRASSMANNIAN LG(3,6)(${\mathbb{K}}$)

Part of: Geometry Linear incidence geometry Finite geometry and special incidence structures Real and complex geometry

Published online by Cambridge University Press:  21 July 2015

J. SCHILLEWAERT  and
H. VAN MALDEGHEM
J. SCHILLEWAERT
Affiliation:
Department of Mathematics, Imperial College, South Kensington Campus, London SW7-2AZ, United Kingdom e-mail: jschillewaert@gmail.com
H. VAN MALDEGHEM
Affiliation:
Department of Mathematics, Ghent University Krijgslaan 281-S22, B-9000 Ghent, Belgium e-mail: hvm@cage.ugent.be
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Abstract

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We provide a combinatorial characterization of LG(3,6)(${\mathbb{K}}$) using an axiom set which is the natural continuation of the Mazzocca–Melone set we used to characterize Severi varieties over arbitrary fields (Schillewaert and Van Maldeghem, Severi varieties over arbitrary fields, Preprint). This fits within a large project aiming at constructing and characterizing the varieties related to the Freudenthal–Tits magic square.

MSC classification

Primary: 51A45: Incidence structures imbeddable into projective geometries
Secondary: 51A50: Polar geometry, symplectic spaces, orthogonal spaces 51E24: Buildings and the geometry of diagrams 51M35: Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 293 - 311
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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