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On the embeddability of polar spaces

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Abstract

We show that every nondegenerate polar space of rank at least 4 with at least three points on each line can be embedded in a projective space. Together with some results from [9] and [12], this provides a particularly elementary proof that any such polar space is of classical type. Our methods involve the use of geometric hyperplanes and work equally well for spaces of finite or infinite rank.

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Authors and Affiliations

  1. Department of Mathematics, Endhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Hans Cuypers

  2. Department of Mathematics, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    Peter Johnson

  3. Department of Mathematics, University of Siena, Via del Capitano 15, 53100, Siena, Italy

    Antonio Pasini

Authors
  1. Hans Cuypers
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  2. Peter Johnson
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  3. Antonio Pasini
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Cuypers, H., Johnson, P. & Pasini, A. On the embeddability of polar spaces. Geom Dedicata 44, 349–358 (1992). https://doi.org/10.1007/BF00181400

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  • DOI: https://doi.org/10.1007/BF00181400

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