On the simple connectedness of hyperplane complements in dual polar spaces |
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| Authors: | I. Cardinali A. Pasini |
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| Affiliation: | a Dipartimento di Scienze Matematiche e Informatiche, Università di Siena, Pian dei Mantellini 44, I-53100 Siena, Italy
b Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 (S22), B-9000 Gent, Belgium |
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| Abstract: | Let Δ be a dual polar space of rank n≥4, H be a hyperplane of Δ and Γ?Δ?H be the complement of H in Δ. We shall prove that, if all lines of Δ have more than 3 points, then Γ is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar spaces, arise from embeddings. |
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| Keywords: | Diagram geometry Dual polar spaces Hyperplanes Simple connectedness Universal embedding |
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