Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
From the reviews:
"The book under review, Algebraic Geometry, by Daniel Perrin, is an introductory text on modern algebraic geometry. It is aimed to be the text for a first basic course for graduate students. ... is very nicely written (and very nicely translated into English too). ... Perrin has included many, many remarks aimed to explain and deconstruct definitions and theorems. I believe these remarks will be very valuable to the reader in order to gain the very much needed intuition for the theory." (Alvaro Lozano-Robledo, MathDL, May, 2008)
"The book under review is the faithful translation into English of D. Perrin's popular French text 'Geometrie algebrique. Une introduction.' ... will be to the greatest benefit of the wide international community of students, teachers, and beginning researchers in the field of modern algebraic geometry. Also, we would like to emphasize again that this primer is perfectly suitable for a one-semester graduate course on the subject, and for profound self-study just as well." (Werner Kleinert, Zentralblatt MATH, Vol. 1132 (10), 2008)
"This is the English translation of an outstanding textbook, originally published in French. ... Appendices contain a summary of results from commutative algebra used in this book and a short introduction to scheme theory. Anyone looking for a textbook on algebraic geometry that starts with the basics and presents a lot of material in a digestible way ... will find this volume an excellent choice." (Ch. Baxa, Monatshefte fur Mathematik, Vol. 160 (4), July, 2010)