Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T09:16:31.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Groups Associated with Certain Loci In [5]

Published online by Cambridge University Press:  20 November 2018

A. F. Horadam
A. F. Horadam*
Affiliation:
University of New England, Armidale, Australia and The University, Leeds, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If x- (i = 1, 2, … , 6) are homogeneous co-ordinates in [5] (the complex projective space of five dimensions), then the equation

1.1

represents the well-known (11) Perazzo cubic primalP43 of order 3 and dimension 4. With it is associated the Segre cubic threefoldS33 (12); specifically, S33 is the section of P43 by a tangent [4].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 113 - 119
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Baker, H. W., Segre's ten nodal cubic primal in space of four dimensions and del Pezzo's surface in five dimensions, J. Lond. Math. Soc, 6 (1931), 176–185.Google Scholar
2. Baker, H. W., Principles of Geometry, vol. 4 (Cambridge, 1950), pp. 148, 151.Google Scholar
3. Bolt, Beverley, Room, T. G., and Wall, G. E., On the Clifford collineation, transform and similarity groups I, II, J. Aust. Math. Soc, 2 (1961), 60–96.Google Scholar
4. Bolt, Beverley, On the Clifford collineation, transform and similarity groups III. Generators and involutions, J. Aust. Math. Soc, 2 (1962), 334–344.Google Scholar
5. Clebsch, A., Leçons sur la géométrie (Paris, 1880), pp. 232–233.Google Scholar
6. Horadam, A. F., A locus in [8] invariant under a group of order 51840 × 81, Quart. J. Math. (Oxford), (2) 8 (1957), 241–259.Google Scholar
7. Horadam, A. F., Projection of an invariant locus in [8] from a solid lying on it, Quart. J. Math. (Oxford), (2) 9 (1958), 81–87.Google Scholar
8. Horadam, A. F., Involutions associated with the Burkhardt configuration in [4], Can. J. Math. 11 (1959), 18–33.Google Scholar
9. Horadam, A. F., Clifford groups in the plane, Quart. J. Math. (Oxford), (2) 10 (1959), 294–295.Google Scholar
10. Horadam, A. F., Clifford matrices and the Hessian group, Rend, del Circ Mat. di Palermo (2), 10 (1961), 347–352.Google Scholar
11. Perazzo, U., Sopra una forma con 9 rette doppie dello spazio a cinque dimensioni, Atti Reale Ace Sci. Torino, 86 (1900-1), 891–916.Google Scholar
12. Segre, C., Sidle varieta cubiche dello spazio a quattro dimensioni e su certi sistemi di rette e certe superficie dello spazio ordinario, Mem. Reale Ace della Scienze Torino, (2) 39 (1889), 3–48.Google Scholar