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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

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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.