algebraic geometry

The author of an introductory book on algebraic geometry has the difficult task of providing geometrical insight and examples, while at the same time developing the modern technical language of the subject. For in algebraic geometry, a great gap appears to separate the intuitive ideas which form the point of departure from the technical methods used in modern research.

The first question is that of language. Algebraic geometry has developed in waves, each with its own language and point of view.