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Caps Embedded in Grassmannians

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Abstract

This paper is concerned with constructing caps embedded in line Grassmannians. In particular, we construct a cap of size q3 +2q2+1 embedded in the Klein quadric of PG(5,q) for even q, and show that any cap maximally embedded in the Klein quadric which is larger than this one must have size equal to the theoretical upper bound, namely q3+2q2+q+2. It is not known if caps achieving this upper bound exist for even q > 2.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, U.S.A. E-mail

    G. L. Ebert

  2. Mathematisches Institut, Arndtstr: 2, D-35392, Giessen, Germany

    K. Metsch & T. Szönyi

Authors
  1. G. L. Ebert
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  2. K. Metsch
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  3. T. Szönyi
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Ebert, G.L., Metsch, K. & Szönyi, T. Caps Embedded in Grassmannians. Geometriae Dedicata 70, 181–196 (1998). https://doi.org/10.1023/A:1004912020519

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  • DOI: https://doi.org/10.1023/A:1004912020519

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