Abstract
ALGEBRAIC geometry, in spite of its beauty and importance, has long been reproached for lacking proper foundations. Great discoveries have been made, especially in Italy, by the intuition of a number of gifted workers, whose insight had been cultivated by a careful study of special cases. But the time for placing the subject on a firm foundation is long overdue, and the delay is seriously hampering progress. For the last twenty years a few geometers, such as Severi, van der Waerden and Zariski, have made important contributions towards this end. Now Prof. Weil has given a connected and comprehensive account of his own and other researches, sufficient to justify the use of intersection-multiplicities, which play such a large part in recent geometry, especially in Italian work. The book is not easy reading, especially for those to whom geometry is synonymous with space-intuition. At a first glance the reader might imagine that it is a treatise on something like abstract algebra. Indeed, the author warns the reader that it is necessary to have a good elementary knowledge of abstract fields and of other topics that will be found in van der Waerden‘s "Moderne Algebra". Apart from this the book is self-contained, and its subject is not abstract algebra, but what might be called abstract geometry.
Foundations of Algebraic Geometry
By Prof. André Weil. (American Mathematical Society: Colloquium Publications, Vol. 29.) Pp. xix+288. (New York: American Mathematical Society, 1946.) 5.50 dollars.
Article PDF
Rights and permissions
About this article
Cite this article
PIAGGIO, H. Foundations of Algebraic Geometry. Nature 161, 787 (1948). https://doi.org/10.1038/161787a0
Issue Date:
DOI: https://doi.org/10.1038/161787a0