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- W4247238216 abstract "A curve Γ has been defined as a normal multiple of a curve C if it contains an involution I n , of order n , which has the properties: (1) the sets of I n are in (1–1) correspondence with the points of C ; (2) each set I n consists of n points which are distinct in the birational sense; (3) I n is generated by an Abelian group G of order n of birational transformations of Γ into itself. We shall denote the field of complex numbers by k , the function field of C by k ( C ), and the function field of Γ by k (Γ). Conditions (1) and (3) imply that k (Γ) is a commutative normal (i.e. Galois) extension of k ( C ). The object of this note is to show how, given the curve C and the Abelian group G of order n , we can construct a curve Γ with the properties (1), (2), (3)." @default.
- W4247238216 created "2022-05-12" @default.
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- W4247238216 date "1946-02-01" @default.
- W4247238216 modified "2023-10-05" @default.
- W4247238216 title "On multiple curves. III." @default.
- W4247238216 doi "https://doi.org/10.1017/s0305004100022672" @default.
- W4247238216 hasPublicationYear "1946" @default.
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