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On the regularity of surfaces, II

Published online by Cambridge University Press:  24 October 2008

L. Roth
Affiliation:
Clare College

Extract

This paper is a sequel to one recently published, in which the regularity of surfaces was investigated by means of certain criteria suggested by Comessatti. We suppose throughout that the surface F under consideration is of general type in Sr, and that it has curve sections C of order n and genus π. It may be recalled that in the previous work the two most useful criteria were the following theorems:

If π < ½ (n + 2), then F is regular or referable. (I)

If πr (n) ≤ π ≤ n, where πr (n) is the maximum genus of a Cn in Sr, then F is regular or referable. (II)

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

REFERENCES

1.Babbage, , Proc. Camb. Phil. Soc. 29 (1933), 212.CrossRefGoogle Scholar
2.Berry, , Trans. Camb. Phil. Soc. 18 (1900), 333;Google Scholar
Berry, , Trans. Camb. Phil. Soc. 19 (1904), 249;Google Scholar
Berry, , Trans. Camb. Phil. Soc. 20 (1908), 74.Google Scholar
3.Castelnuovo, , Atti Acc. Torino, 24 (1889), 346.Google Scholar
4.Castelnuovo, , Atti Acc. Torino, 25 (1890), 695.Google Scholar
5.Castelnuovo-Enriques, , Annali di Mat. (3), 6 (1901), 165.CrossRefGoogle Scholar
6.Comessatti, , Atti Ist. Veneto (8), 17 (1915)2, 296.Google Scholar
7.Comessatti, , Mem. Soc. Ital. Scienze (3), 21 (1919), 45.Google Scholar
8.Val, Du, Journal Lond. Math. Soc. 8 (1933), 11.CrossRefGoogle Scholar
9.Enriques, , Lezioni sulla teoria delle superficie algebriche, Padova (1932).Google Scholar
10.Enriques-Severi, , Acta Math. 32 (1909), 283.CrossRefGoogle Scholar
11.Fano, , Memorie Acc. Torino (2), 44 (1894), 335.Google Scholar
12.Humbert, , Journ. de Math. (4), 9 (1893), 361.Google Scholar
13.Noether, , Abhandlungen Akad. Wiss. Berlin (1883), 80.Google Scholar
14.Roth, , Proc. Camb. Phil. Soc. 30 (1934), 4.CrossRefGoogle Scholar
15.Semple, , Proc. Lond. Math. Soc. (2), 32 (1932), 200.Google Scholar
16.Severi, , Rend. Lincei (5), 15 (1906)2, 691.Google Scholar
17.Severi, , Rend. Palermo, 17 (1903), 73.CrossRefGoogle Scholar