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On the highest space in which a non-ruled surface of given order can lie

Published online by Cambridge University Press:  20 January 2009

G. Timms
G. Timms
Affiliation:
The University, St Andrews.
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Extract

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It is well known that a non-ruled (i.e. not consisting of an infinity of lines) surface of order n lies in a space of not more than n dimensions n ≠ 4) and that for n > 9, the maximum dimension actually attained (here denoted by R) is certainly less than n.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 6 , Issue 3 , August 1940 , pp. 149 - 150
Copyright
Copyright © Edinburgh Mathematical Society 1940

References

page 149 note 1 Del Pezzo, , Rend. R. Ace. Napoli, 24 (1885), 215, and 25 (1886), 208.Google Scholar

page 149 note 2 Rend. R. Acc. Napoli (3), 30 (1924), 80.Google Scholar

page 150 note 1 The prime sections are evidently hypeielliptic. The same surfaces, when In is an integer, are in fact those having the maximum order for a given genus of section.