Algebraic geometry and commutative algebra / Siegfried Bosch

The main purpose of the book is to introduce the basic concepts and methods of modern algebraic geometry to novices in the field, requiring just a solid knowledge of linear algebra as a prerequisite. More precisely, the author’s intention is to explain some foundational principles of A. Grothendieck’s theory of algebraic schemes and their morphisms, together with the necessary (and closely related) background material from commutative algebra. As the author points out in the preface, the present text grew out of his repeated courses and seminars on the subject, which usually consisted of one semester of commutative algebra and then continued with two semesters of scheme-theoretic algebraic geometry. In this approach, commutative algebra is treated as a separate first part, while the second part deals with four selected, general topics in algebraic geometry based on just that commutative-algebraic framework. ...(Zentralblatt)