The common curve of quadrics sharing a self-polar simplex
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.
KeywordsProjective Space Common Curve Consequent Property
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- H. F. Baker,Principles of geometry, Cambridge, vol. IV, 1925.Google Scholar
- G. Salmon,A treatise on the analytic geometry of three dimensions, 4th ed., Dublin, 1882.Google Scholar
- 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
- F. Severi,Lezioni di geometria algebrica, Padua, 1908.Google Scholar
- 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