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Published online by Cambridge University Press: 24 October 2008
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.
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† The partial systems in both (i) and (ii) are, if necessary, augmented by fixed parts.
* Baker, loc. cit. p. 285.