The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text and added new material. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of the first volume and is suitable for beginning graduate students.
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Language Notes
Text: English (translation)
Original Language: Russian
Original Language: Russian
From the Back Cover
Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. 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 Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of algebraic and complex-analytic geometry in different areas of mathematics and theoretical physics should be grateful to the author for his renewed service to the mathematical community."
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Most Helpful Customer Reviews
4 of 6 people found the following review helpful:
5.0 out of 5 stars
Are you looking for literary criticism? It's a freaking math book!,
This review is from: Basic Algebraic Geometry 2: Schemes and Complex Manifolds (Paperback)
The first book in this two volume introduction to algebraic geometry was used as the primary textbook for my algebraic geometry class. It was amazing. Easily the most readable (oh, Hartshorne why are you so heartless?) of all the algebraic algebraic geometry I own (which is quite a few). I finally managed to secure the second volume after several fruitless searches and order cancellations (Amazon didn't have it in stock for months). Though I'm only starting to get into this one and am basing this recommendation mostly on my experience with the first volume, I still think that Shafarevich writes the most accessible introduction to schemes that I've ever read.
1 of 14 people found the following review helpful:
3.0 out of 5 stars
Was the book modified without modifying the index?,
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This review is from: Basic Algebraic Geometry 2: Schemes and Complex Manifolds (Paperback)
Shafarevich explains mathematics well, but I find the index for this book extremely frustrating (I bought my copy in the 2005 Springer sale). I'm almost convinced that they forgot to modify the index after making modifications to the first edition.
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Inside This Book
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First Sentence:
In this chapter, we return to the starting point of all our study - the notion of algebraic variety - and attempt to look at it from a more general and invariant point of view. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
meromorphic fractions, principal open sets, compatible triangulations, nonsingular projective curve, quasiprojective varieties, affine neighbourhood, unramified cover, combinatorial surface, complete algebraic variety, quasiprojective variety, ringed spaces, closed subscheme, holomorphic differential form, ramification degree, affine open sets, nonsingular variety, fundamental polygon, affine schemes, structure sheaf, coherent sheaf, compact complex surfaces, algebraic family, higher dimensional varieties, invertible sheaves, irreducible algebraic variety Key Phrases - Capitalized Phrases (CAPs): (learn more)
Find the Hilbert, Grassmannian Grass New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter, we return to the starting point of all our study - the notion of algebraic variety - and attempt to look at it from a more general and invariant point of view. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
meromorphic fractions, principal open sets, compatible triangulations, nonsingular projective curve, quasiprojective varieties, affine neighbourhood, unramified cover, combinatorial surface, complete algebraic variety, quasiprojective variety, ringed spaces, closed subscheme, holomorphic differential form, ramification degree, affine open sets, nonsingular variety, fundamental polygon, affine schemes, structure sheaf, coherent sheaf, compact complex surfaces, algebraic family, higher dimensional varieties, invertible sheaves, irreducible algebraic variety Key Phrases - Capitalized Phrases (CAPs): (learn more)
Find the Hilbert, Grassmannian Grass New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
See all 10 books this book cites
- The Red Book (Learning Language Arts Through Literature) by Common Sense Press in Back Matter
- The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics) by David Mumford in Back Matter
- Local Analytic Geometry by Shreeram Shankar Abhyankar in Back Matter
- Differentiable Manifolds (Grundlehren Der Mathematischen Wissenschaften) by Georges De Rham on page 119
- Algebraic Geometry (Dover Books on Mathematics) by Solomon Lefschetz in Back Matter
See all 10 books this book cites
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