Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-30T00:01:54.865Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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