2 results
A COMBINATORIAL CHARACTERIZATION OF THE LAGRANGIAN GRASSMANNIAN LG(3,6)(
${\mathbb{K}}$)
- Part of
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- Journal:
- Glasgow Mathematical Journal / Volume 58 / Issue 2 / May 2016
- Published online by Cambridge University Press:
- 21 July 2015, pp. 293-311
- Print publication:
- May 2016
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- Article
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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.
Regular Embeddings of Generalized Hexagons
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- Journal:
- Canadian Journal of Mathematics / Volume 56 / Issue 5 / 01 October 2004
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1068-1093
- Print publication:
- 01 October 2004
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- Article
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We classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type
${{\text{G}}_{2}}$, 
${}^{3}{{\text{D}}_{4}}$ and 
${}^{6}{{\text{D}}_{\text{4}}}$
(and occurring in projective dimensions 5, 6, 7), we find new examples in unbounded dimension related to the mixed groups of type
${{\text{G}}_{2}}$
.
