ABSTRACT
1. Since 1960, there has been a tremendous increase in the number of mathe maticians who are working in algebraic geometry. A summer institute held in California in 1974 was attended by 270 mathematicians! This phenomenon can be attributed on one hand to the unusual wealth and diversity of (old and new) interesting and “natural” problems afforded by algebraic geometry, and to their multiple connections with number theory, analytic geometry, and analysis, and on the other hand to the availability of powerful and easy-to-grasp techniques of attack, with no need for an appeal to some personal and more or less reliable “intuition.”
