Summary
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.
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References
H. F. Baker,Principles of geometry, Cambridge, vol. IV, 1925.
W. L. Edge,Humbert's plane sextics of genus 5, Proceedings of the Cambridge Philosophical Society,47 (1951), pp. 483–495.
W. L. Edge,Three plane sextics and their automorphisms, Canadian Journal of Mathematics,21 (1969), pp. 1263–1278.
W. L. Edge,The principal chords of an elliptic quartic, Proceedings of the Royal Society of Edinburgh (A)71 (1972), pp. 43–50.
W. L. Edge,The osculating spaces of a certain curve in [n], Proceedings of the Edinburgh Mathematical Society (2)19 (1974), pp. 39–44.
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.
G. Salmon,A treatise on the analytic geometry of three dimensions, 4th ed., Dublin, 1882.
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.
F. Severi,Sopra alcune singolarità delle curve di un iperspazio, Memorie Accad. Scienze di Torino,2 (1902), pp. 81–114.
F. Severi,Lezioni di geometria algebrica, Padua, 1908.
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.
H. G. Zeuthen,Nouvelle démonstration de théorèmes sur des séries de points correspondants sur deux courbes, Mathematische Annalen,3 (1871), pp. 150–156.
H. G. Zeuthen,Lehrbuch der abzählenden Methoden der Geometrie, Teubner, Leipzig and Berlin, 1914.
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Entrata in Redazione il 23 giugno 1976.
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Edge, W.L. The common curve of quadrics sharing a self-polar simplex. Annali di Matematica 114, 241–270 (1977). https://doi.org/10.1007/BF02413789
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DOI: https://doi.org/10.1007/BF02413789