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An extension of a fundamental theorem in the theory of surfaces

Published online by Cambridge University Press:  24 October 2008

D. Pedoe
Affiliation:
Magdalene College

Extract

1. In a paper by Castelnuovo and Enriques the following fundamental theorem is proved:.

“An algebraic surface containing a linear system of curves of freedom r ≥ 0, genus π > 0, and grade n > 2π − 2 is necessarily scrollar.”

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Annali di Mat. (3), 6 (1901), 165225.Google Scholar

I.e. rational or referable to a ruled surface.

I.e. computed. See Enriques, , Lezioni sulla teoria delle superficie algebriche (Padova, 1932), 61.Google Scholar

§ Campedelli, , Rendiconti Lincei (6), 18 (1933), 377381.Google Scholar

See Part c of Campedelli's paper.

Castelnuovo, , Annali di Mat. (2) 25 (1897), 235318.CrossRefGoogle Scholar