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- W1539294583 abstract "An embedding of a point-line geometry (varGamma ) is usually defined as an injective mapping (varepsilon ) from the point-set of (varGamma ) to the set of points of a projective space such that (varepsilon (l)) is a projective line for every line (l) of (varGamma ). However, different situations are considered in the literature, where (varepsilon (l)) is allowed to be a subline of a projective line or a curve. In this paper we propose a more general definition of embedding which includes all the above situations and we focus on a class of embeddings, which we call Grassmann embeddings, where the points of (varGamma ) are firstly associated to lines of a projective geometry ({mathrm {PG}}(V)), next they are mapped onto points of ({mathrm {PG}}(Vwedge V)) via the usual projective embedding of the line-grassmannian of ({mathrm {PG}}(V)) in ({mathrm {PG}}(Vwedge V)). In the central part of our paper we study sets of points of ({mathrm {PG}}(Vwedge V)) corresponding to lines of ({mathrm {PG}}(V)) totally singular for a given alternating, hermitian or quadratic form of (V). Finally, we apply the results obtained in that part to the investigation of Grassmann embeddings of several generalized quadrangles." @default.
- W1539294583 created "2016-06-24" @default.
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- W1539294583 date "2014-01-01" @default.
- W1539294583 modified "2023-09-27" @default.
- W1539294583 title "Embeddings of Line-Grassmannians of Polar Spaces in Grassmann Varieties" @default.
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- W1539294583 doi "https://doi.org/10.1007/978-81-322-1814-2_4" @default.
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