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.
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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." (Álvaro Lozano-Robledo, MathDL, May, 2008) "The book under review is the faithful translation into English of D. Perrin’s popular French text ‘Géométrie algébrique. 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)
From the Back Cover
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 and assumes only the standard background of undergraduate algebra. It is developed from a masters course given at the Université Paris-Sud, Orsay, and focusses on projective algebraic geometry over an algebraically closed base field. The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. 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.
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5 of 5 people found the following review helpful:
4.0 out of 5 stars
one of the best introductory books,
By R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Algebraic Geometry: An Introduction (Universitext) (Paperback)
Although not in every way an easy book,
this book has both great examples and discussion of ideals, schemes, modules, rings and sheaves. Projective spaces and algebraic varieties seem to bridge gaps in the traditional analytic geometry approach to curves. I suppose that a better coverage of the theory of duals would have helped me more, but there is a lot of the stuff needed in this book.The coverage of genus arguments is better than that of Hilbert Polynomials. The coverage the connection between parametric and implicit curves is what sold me on this book.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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standard open sets, infinitesimal neighbours, irreducible projective algebraic variety, open affine sets, irreducible affine algebraic variety, projective algebraic set, affine algebraic set, structural sheaf, geometric genus, finite scheme, open affine subset, irreducible projective curve, arithmetic genus, saturated ideal, ringed space, projective plane curve, dominant morphism, affine open sets, irreducible algebraic variety, algebraic sets, gluing condition, irreducible subsets, irreducible algebraic varieties, minimal resolution, affine algebraic varieties Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Veronese Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
standard open sets, infinitesimal neighbours, irreducible projective algebraic variety, open affine sets, irreducible affine algebraic variety, projective algebraic set, affine algebraic set, structural sheaf, geometric genus, finite scheme, open affine subset, irreducible projective curve, arithmetic genus, saturated ideal, ringed space, projective plane curve, dominant morphism, affine open sets, irreducible algebraic variety, algebraic sets, gluing condition, irreducible subsets, irreducible algebraic varieties, minimal resolution, affine algebraic varieties Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Veronese Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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