Classical Algebraic Geometry: A Modern View

Abstract

The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times. Often in the history of mathematics new ideas and techniques make the work of previous generations of researchers obsolete, especially this applies to the foundations of the subject and the fundamental general theoretical facts used heavily in research. Even the greatest achievements of the past genera-tions which can be found for example in the work of F. Severi on algebraic cycles or in the work of O. Zariski’s in the theory of algebraic surfaces have been greatly generalized and clarified so that they now remain only of histor-ical interest. In contrast, the fact that a nonsingular cubic surface has 27 lines or that a plane quartic has 28 bitangents is something that cannot be improved upon and continues to fascinate modern geometers. One of the goals of this present work is then to save from oblivion the work of many mathematicians who discovered these classic tenets and many other beautiful results.

The authors' abstract, as published at the source., 2012 · DOI ↗