Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-06T03:50:55.912Z Has data issue: false hasContentIssue false

The algebraic surfaces contained by a cubic primal in four dimensions

Published online by Cambridge University Press:  24 October 2008

J. W. Archbold
Affiliation:
St John's College

Extract

1. In this note we investigate, from a new point of view, some properties of cubic primals in [4]. These are enunciated by Fano as follows.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1933

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

* Fano, , “Sulle superficie algebriche contenute in una varietà cubica dello spazio a quattro dimensioni”, Atti Torino 39 (19031904), 597.Google Scholar

Severi, , “Alcune relazioni di equivalenza tra gruppi di punti d' una curva algebrica o tra curve di una superficie”, Atti Veneto 70 (19101911), 373.Google Scholar

Segre, , “Sulle varietà cubiche dello spazio a quattro dimensioni e su certi sistemi di rette e certe superficie dello spazio ordinario”, Mem. Torino (2) 39 (1887), 3.Google Scholar

* White, F. P., “The projective generation of curves and surfaces in space of four dimensions”, Proc. Camb. Phil. Soc. 21 (1922) 216227 (219).Google Scholar

Segre, loc. cit. § 14.

The surfaces on M corresponding to the curves of order μ in π form an algebraic system which, since M is rational, belongs to a linear system.

* Severi, , “Fondamenti per la geometria sulle varietà algebriche”, Rend. Palermo 28 (1909), 3387 (§2).CrossRefGoogle Scholar

Consideration of a prime section of M shows that A n + Ψ ≡ F is false.