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Varieties representing certain systems of Schubert triangles

Published online by Cambridge University Press:  26 February 2010

P. S. Haskell
P. S. Haskell
Affiliation:
Portsmouth College of Technology.
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Extract

There are many convenient ways in which a plane triangle can be defined and given projective coordinates. It can most simply be treated as an ordered triad of points (A, B, C) or dually as an ordered triad of lines (a, b, c), but it may seem more natural to regard it as a triad of points and an associated triad of lines which together satisfy the familiar incidence conditions. Again, the triangle for which Schubert [1] developed a calculus was a septuple, but Semple [2] has shown the advantages of a calculus for a triangle defined as an octuple.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 151 - 160
Copyright
Copyright © University College London 1967

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References

1.Schubert, H., “Anzahlgeometrische Behandlung des Dreiecks”, Math. Ann., 17 (1880), 153–212.Google Scholar
2.Semple, J. G., “The triangle as a geometric variable”, Mathematika, 1 (1954), 80–88.Google Scholar
3.Haskell, P. S., The foundations and development of the enumerative geometry of triangles (Ph.D. Thesis, London University, 1963).Google Scholar
4.Tyrrell, J. A., “On infinitesimal triangles”, Mathematika, 7 (1960), 10–14.Google Scholar