This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
Elementary Algebraic Geometry
This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric.
This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.
This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs.
This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.
"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way.
In: Proceedings of the 1984 Vancouver Conference in Algebraic Geometry. CMS Conference Proceedings, pp. 163–226. The American Mathematical Society, Providence (1986) 33. Kosters, M.: Injective modules and the injective hull of a module.
The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter. This book consists of two parts.
Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kahler geometry.
The book then turns to several applications of the enumerative formulas and universal identity, including including enumerative proofs of the straightening law of Doubilet-Rota-Stein and computations of Hilbert functions of polynomial ...