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Advances in Geometry

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Pseudo-embeddings of the (point, k-spaces)-geometry of PG(n, 2) and projective embeddings of DW(2n − 1, 2)

Bart De Bruyn
Published Online: 2018-03-26 | DOI: https://doi.org/10.1515/advgeom-2017-0065


We classify all homogeneous pseudo-embeddings of the point-line geometry defined by the points and k-dimensional subspaces of PG(n, 2), and use this to study the local structure of homogeneous full projective embeddings of the dual polar space DW(2n − 1, 2). Our investigation allows us to distinguish n possible types for such homogeneous embeddings. For each of these n types, we construct a homogeneous full projective embedding of DW(2n − 1, 2).

Keywords: Homogeneous projective embedding; (symplectic) dual polar space; pseudo-embedding; pseudo-hyperplane

MSC 2010: 05B25; 51A45; 51A50


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About the article

Received: 2016-11-03

Published Online: 2018-03-26

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0065.

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