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The algebraic surfaces contained by a cubic primal in four dimensions
Published online by Cambridge University Press: 24 October 2008
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
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 4 , 30 October 1933 , pp. 484 - 486
- Copyright
- Copyright © Cambridge Philosophical Society 1933
References
* Fano, , “Sulle superficie algebriche contenute in una varietà cubica dello spazio a quattro dimensioni”, Atti Torino 39 (1903–1904), 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 (1910–1911), 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) 216–227 (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), 33–87 (§2).CrossRefGoogle Scholar
† Consideration of a prime section of M shows that A n + Ψ ≡ F is false.