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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
D. Pedoe
Affiliation:
Magdalene College
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 4 , October 1934 , pp. 409 - 411
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Annali di Mat. (3), 6 (1901), 165–225.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), 377–381.Google Scholar

∥ See Part c of Campedelli's paper.

Castelnuovo, , Annali di Mat. (2) 25 (1897), 235–318.CrossRefGoogle Scholar