Annali di Matematica Pura ed Applicata

, Volume 114, Issue 1, pp 241–270 | Cite as

The common curve of quadrics sharing a self-polar simplex

  • W. L. Edge


When n-1 quadrics in projective space [n] of n dimensions have a common self-polar simplex their common curve Γ admits a group of2 n self-projectivities. The consequent properties of Γ are investigated, and further specialisations are imposed which amplify the the group and endow Γ with further properties. There is some reference to the osculating spaces and principal chords of Γ, and some properties of particular curves in four and five dimensions are described.


Projective Space Common Curve Consequent Property 
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  1. [1]
    H. F. Baker,Principles of geometry, Cambridge, vol. IV, 1925.Google Scholar
  2. [2]
    W. L. Edge,Humbert's plane sextics of genus 5, Proceedings of the Cambridge Philosophical Society,47 (1951), pp. 483–495.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    W. L. Edge,Three plane sextics and their automorphisms, Canadian Journal of Mathematics,21 (1969), pp. 1263–1278.zbMATHMathSciNetGoogle Scholar
  4. [4]
    W. L. Edge,The principal chords of an elliptic quartic, Proceedings of the Royal Society of Edinburgh (A)71 (1972), pp. 43–50.MathSciNetGoogle Scholar
  5. [5]
    W. L. Edge,The osculating spaces of a certain curve in [n], Proceedings of the Edinburgh Mathematical Society (2)19 (1974), pp. 39–44.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    W. L. Edge,The chord locus of a certain curve in [n], Proceedings of the Royal Society of Edinburgh (A)71 (1973), pp. 337–343.MathSciNetGoogle Scholar
  7. [7]
    G. Salmon,A treatise on the analytic geometry of three dimensions, 4th ed., Dublin, 1882.Google Scholar
  8. [8]
    C. Segre,Introduzione alla geometria sopra un ente algebrico semplicemente infinito, Annali di matematica (2)22 (1894), pp. 41–142; Opere, vol. I, Rome, 1957, pp. 198–304.Google Scholar
  9. [9]
    F. Severi,Sopra alcune singolarità delle curve di un iperspazio, Memorie Accad. Scienze di Torino,2 (1902), pp. 81–114.zbMATHGoogle Scholar
  10. [10]
    F. Severi,Lezioni di geometria algebrica, Padua, 1908.Google Scholar
  11. [11]
    A. Wiman,Über die algebraischen Curven von den Geschlectern p=4, 5 und 6, welche eindeutige Transformationen in sich besitzen, Svenska Vet-Akad. Handlingar, Bihang till Handlingar21 (1895), afd. 1, no. 3, 41 pp.Google Scholar
  12. [12]
    H. G. Zeuthen,Nouvelle démonstration de théorèmes sur des séries de points correspondants sur deux courbes, Mathematische Annalen,3 (1871), pp. 150–156.CrossRefMathSciNetGoogle Scholar
  13. [13]
    H. G. Zeuthen,Lehrbuch der abzählenden Methoden der Geometrie, Teubner, Leipzig and Berlin, 1914.zbMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • W. L. Edge
    • 1
  1. 1.EdinburghGran Bretagna

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