Pencilled regular parallelisms

Preprint English OPEN
Havlicek, Hans; Riesinger, Rolf;
(2017)
  • Subject: Mathematics - Rings and Algebras | 51A15, 51M30 | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Algebraic Geometry

Over any field $\mathbb K$, there is a bijection between regular spreads of the projective space ${\rm PG}(3,{\mathbb K})$ and $0$-secant lines of the Klein quadric in ${\rm PG}(5,{\mathbb K})$. Under this bijection, regular parallelisms of ${\rm PG}(3,{\mathbb K})$ cor... View more
  • References (28)
    28 references, page 1 of 3

    [1] W. Benz, Classical Geometries in Modern Contexts. Birkhauser, Basel 2007.

    [2] A. Betten, The packings of PG(3; 3). Des. Codes Cryptogr. 79 (2016), 583{595.

    [3] D. Betten, R. Lowen, Compactness of the automorphism group of a topological parallelism on real projective 3-space. Preprint (arXiv:1702.02837), 2017.

    [4] D. Betten, R. Riesinger, Topological parallelisms of the real projective 3-space. Results Math. 47 (2005), 226{241.

    [5] D. Betten, R. Riesinger, Constructing topological parallelisms of PG(3; R) via rotation of generalized line pencils. Adv. Geom. 8 (2008), 11{32.

    [6] D. Betten, R. Riesinger, Hyper ock determining line sets and totally regular parallelisms of PG(3; R). Monatsh. Math. 161 (2010), 43{58.

    [7] D. Betten, R. Riesinger, Cli ord parallelism: old and new de nitions, and their use. J. Geom. 103 (2012), 31{73.

    [8] D. Betten, R. Riesinger, Automorphisms of some topological regular parallelisms of PG(3; R). Results Math. 66 (2014), 291{326.

    [9] A. Blunck, A. Herzer, Kettengeometrien { Eine Einfuhrung. Shaker Verlag, Aachen 2005.

    [10] A. Blunck, S. Pasotti, S. Pianta, Generalized Cli ord parallelisms. Quad. Sem. Mat. Brescia 20 (2007), 1{13.

  • Similar Research Results (1)
  • Metrics
Share - Bookmark