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The Relations between the Invariants of Two Surfaces in (1, n) Cyclic Correspondence
Published online by Cambridge University Press: 24 October 2008
Extract
On a surface F′ an algebraic self-correspondence T of period n defines a cyclic involution In of sets of n points. Then if there exists a surface F whose points are in (1, 1) correspondence with the sets of In, the surfaces F, F′ will be said to be in (1, n) cyclic correspondence. The purpose of the present paper is to show that, when n is a prime number and with certain restrictions upon the united curve of the self-correspondence T, the irregularities of the surfaces F and F′ are equal.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 1 , January 1936 , pp. 23 - 29
- Copyright
- Copyright © Cambridge Philosophical Society 1936
References
* Severi, , “Relazioni che legano i caratteri invarianti di due superficie in corrispondenza algebrica”, Rend. Lombardi (11), 36 (1903), 495–511.Google Scholar
† Severi, loc. cit. p. 509.
* See Godeaux, , “Recherches sur les involutions doués d'un nombre fini de points de coincidence”, Bull. Soc. Math. de France, 47 (1919), 1–16.Google Scholar
† Baker, , Principles of Geometry, 6, 140, 224.Google Scholar
‡ Picard-Simart, , Fonctions algébriques de deux variables, 2 (1906), 438.Google Scholar
* Baker, loc. cit. p. 269.
† The partial systems in both (i) and (ii) are, if necessary, augmented by fixed parts.
* Baker, loc. cit. p. 285.