Abstract
IN discussing algebraic curves and surfaces we have the choice of several distinct methods. Some authors rely upon Cremona transformations, by which the curve or surface is brought into correspondence with another and simpler curve or surface. Others rely upon invariant theory, reducing the geometry to algebra. A third school uses parametric representation. It is well known how easily the properties of conies are derived by expressing the co-ordinates of their points as rational or trigonometrical functions of a parameter. For certain cubics, we use elliptic (that is, doubly-periodic) functions. When we come to curves of higher orders we need theta functions, which are multiply-periodic. Some complications arise from the fact that such functions necessarily involve more than one parameter, and are connected by a large number of complicated equations.
Algebraic Geometry and Theta Functions.
By Prof. Arthur B. Coble. (American Mathematical Society Colloquium Publications, Vol. 10.) Pp. vii + 282. (New York: American Mathematical Society; Cambridge: Bowes and Bowes; Berlin: Hirschwaldsche Buehhandlung, 1929.) 3 dollars.
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H. P., H. Algebraic Geometry and Theta Functions . Nature 125, 775 (1930). https://doi.org/10.1038/125775b0
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DOI: https://doi.org/10.1038/125775b0