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A deduction of the formula for the product of two incidence symbols in the case of lines and planes

Published online by Cambridge University Press:  24 October 2008

J. A. Todd
J. A. Todd
Affiliation:
Trinity College
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Extract

The object of this paper is to give proofs of formulae, previously obtained by Schubert (for lines) and Palatini (for planes) by degeneration methods, by a direct application of the coincidence formulae of Pieri and Severi which are referred to below. In the case of planes the essential part of the proof is the deduction of the relation (10) below, from which the required formulae follow directly. The formulae in question have as their object the expression of a product of two incidence conditions as the sum of a number of simple ones.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 4 , October 1929 , pp. 384 - 389
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

* Schubert, , Math. Ann. 26 (1885), p. 26.CrossRefGoogle Scholar

† Palatini, and Giambelli, , Atti Acc. Torino, 36 (1900–1901), p. 476.Google Scholar

‡ For proofs see the first few chapters of Bertini: Introduzione alla geometria proiettiva degli iperspazi (Messina, 1923).Google Scholar

* Pieri, , Atti Acc. Torino, 25 (1890), p. 365.Google Scholar

* Severi, , Rend. Acc. Lincei, (5) 9 (1900)2, p. 321.Google Scholar

† Rend. 1st. Lomb. (2) 27 (1894), p. 258.Google Scholar

‡ Mem. Acc. Torino, (2) 52 (1902) p. 171.Google Scholar

§ Atti Acc. Torino, 36 (1900–1901) p. 476.Google Scholar