Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T08:17:41.339Z Has data issue: false hasContentIssue false

Geometry related to the key del Pezzo surface and the associated mapping of plane cubics

Published online by Cambridge University Press:  14 November 2011

W. L. Edge
Affiliation:
Montagu House, 67 Mill Hill, Musselburgh, East Lothian, EH21 7RL

Synopsis

When the points of a projective space [9] map ternary cubics the maps of perfect cubes are the points of a del Pezzo surface F. Several manifolds linked with F are listed and the cubics mapped on these are noted. A new approach leads to the first of Aronhold's two invariants.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1987

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

1Aronhold, S.. Zur Theorie der homogenen Functionen dritten Grades von drei Variablen. J. Math. 39 (1849), 140159.Google Scholar
2Baker, H. F.. Principles of Geometry VI (London: Cambridge University Press, 1933).Google Scholar
3Bertini, E.. Introduzione alia geometria proiettiva degli iperspazi (Messina, 1923).Google Scholar
4Clebsch, A.. Uber Curven vierter Ordnung. J. Math. 59 (1861), 125145.Google Scholar
5Pezzo, P. del. Sugli spazi tangenti ad una superficie o ad una varieta immersa in uno spazio di piu dimensioni. Rend. Ace. Napoli 25 (1886), 176180.Google Scholar
6Edge, W. L.. Sylvester's unravelment of a ternary quartic. Proc. Roy. Soc. Edinburgh Sect. A 61 (1942), 247259.Google Scholar
7Edge, W. L.. The pairing of del Pezzo quintics. J. London Math. Soc. (2) 27 (1983), 402412.CrossRefGoogle Scholar
8Enriques, F. and Chisini, O.. Teoria geometrica delle equazioni e delle funzioni algebriche II (Bologna: Nicola Zannichelli, 1918).Google Scholar
9Grace, J. H. and Young, A.. The algebra of invariants (London: Cambridge University Press, 1903).Google Scholar
10Salmon, G.. A treatise on the higher plane curves (Dublin: Hodges and Smith, 1852).Google Scholar
11Salmon, G.. Lessons introductory to the modern higher algebra, 3rd edition (Dublin: Hodges, Foster, and Co., 1876).Google Scholar
12Salmon, G.. A treatise on conic sections, 6th edition (London: Longmans, Green, and Co., 1879).Google Scholar
13Semple, J. G. and Roth, L.. Introduction to algebraic geometry (Oxford: Oxford University Press, 1949).Google Scholar
14Sylvester, J. J.. On the principles of the calculus of forms. Cambridge and Dublin Math. J. 7 (1852), 82–97; Mathematical Papers I, 284–327.Google Scholar
15Timms, G.. The nodal cubic surfaces and the surfaces from which they are derived by projection. Trans. Roy. Soc. London A119 (1928), 213248.Google Scholar