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1. Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne | |
Paperback: 516
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 1441928073 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
this is a wonderful book by a master
A Necessary and Useful Pain
Unfortunately a better book on the subject doesn't exist.
Nice selection of exercises
THE book for the Grothendieck approach Some helpful suggestions from my experience with this book: |
2. Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) (Student Mathematical Library, V. 20) by Klaus Hulek | |
Paperback: 213
Pages
(2003-02-13)
list price: US$37.00 -- used & new: US$33.00 (price subject to change: see help) Asin: 0821829521 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 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. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry. Customer Reviews (1)
Trees, not forest |
3. Basic Algebraic Geometry 1: Varieties in Projective Space by Igor R. Shafarevich | |
Paperback: 304
Pages
(1994-08-08)
list price: US$84.95 -- used & new: US$64.79 (price subject to change: see help) Asin: 3540548122 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry. Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities. Customer Reviews (3)
the most geometric, user friendly book on algebraic geometry
Someone hasn't read the first page of the index!!!!!!
After Hartshorne!!! |
4. Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics) by Patrice Tauvel, Rupert W. T. Yu | |
Paperback: 653
Pages
(2010-11-30)
list price: US$115.00 -- used & new: US$115.00 (price subject to change: see help) Asin: 3642063330 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters. |
5. Introduction to Algebraic Geometry by Brendan Hassett | |
Paperback: 264
Pages
(2007-05-21)
list price: US$38.99 -- used & new: US$24.56 (price subject to change: see help) Asin: 0521691419 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Nice
Wait for 2nd Edition
The bookat least cracks the door open? |
6. Using Algebraic Geometry (Graduate Texts in Mathematics) by David A. Cox, John Little, Donal O'Shea | |
Paperback: 558
Pages
(2005-03-17)
list price: US$54.95 -- used & new: US$38.81 (price subject to change: see help) Asin: 0387207333 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Good introduction In general this is a good book and worth reading, if one needs an introduction to the areas covered. Students could definitely benefit from its perusal.
Don't bother |
7. Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics, 6) by Qing Liu | |
Hardcover: 592
Pages
(2002-07-18)
list price: US$134.99 -- used & new: US$94.49 (price subject to change: see help) Asin: 0198502842 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Algebraic Geometry and Arithmetic
Very good exposition The book starts off with a chapter on some topics in basic commutative algebra - localisation, flatness and completion. Once this is done, the stage is set to introduce schemes in the next chapter and prove their basic properties. Chapter 3 talks about morphisms of schemes and base change. Chapter 4 continues with a discussion of morphisms and also presents some results about some special types of schemes (normal, regular). It culminates with a proof of Zariski's main theorem.The next chapter takes up sheaf cohomology and is followed up with a chapter on differential calculus on schemes (Kahler differentials, duality theory). Lastly, chapter 7 takes up divisors, proves the Riemann Roch theorem and culminates with some applications to curves. At a first glance, this would basically look like Hartshorne - the most popular book for an introduction to schemes. However, there are few differences which I will point out. Firstly, Hartshorne emphasizes geometric applications and, as such, uses algebraically closed fields freely. Liu, on the other hand, does not hesistate to give arithmetic applications whenever possible and, therefore, tries to relax the hypotheses on the base field whenever possible. Secondly, Liu is much more readable than Hartshorne which, in its supreme elegance, is a tad dense for a first reading. Unlike Hartshorne, a majority of important results are not presented in the exercises (though many are!). Moreover, unlike Harshorne, this book develops all the necessary commutative algebra along the way (chapter 1,2 of Atiyah-Macdonald should be good enough to read this book). Coming back to the geometry, Hartshorne's chapter 4,5 form an excellent resource for classical geometric applications for theory of schemes. Moreover, chapter 1 presents a very readable and scheme-free account of classical algebraic geometry (pre-Grothendieck) in the language of varieties. Liu's book, however, does not emphasize classical or geometric applications and is not the best place to start if one wishes to learn about varieties. |
8. Fourier-Mukai Transforms in Algebraic Geometry (Oxford Mathematical Monographs) by Daniel Huybrechts | |
Hardcover: 280
Pages
(2006-06-29)
list price: US$125.00 -- used & new: US$107.85 (price subject to change: see help) Asin: 0199296863 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
9. Computational Methods in Commutative Algebra and Algebraic Geometry (Algorithms and Computation in Mathematics) by Wolmer Vasconcelos | |
Paperback: 408
Pages
(2004-07-12)
list price: US$89.95 -- used & new: US$11.04 (price subject to change: see help) Asin: 3540213112 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description From the reviews: |
10. Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin | |
Paperback: 332
Pages
(2008-02-04)
list price: US$46.99 -- used & new: US$37.92 (price subject to change: see help) Asin: 0521718015 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
11. An Invitation to Algebraic Geometry (Universitext) by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves | |
Paperback: 184
Pages
(2010-11-02)
list price: US$59.95 -- used & new: US$48.31 (price subject to change: see help) Asin: 1441931953 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
very good
Splendid introduction
enjoyable guidance
Wow! The only book like this one in brevity and scope is Reid UNDERGRADUATE ALGEBRAIC GEOMETRY--with its highly informed, highly polemical, final chapter on the state of the art. Both are very good. This one is more advanced. Beyond what Reid covers, Smith sketches Hilbert polynomials, Hironaka's (and very briefly even De Jong's) approach to removing singularities, and ample line bundles. You do need a bit of topology and analysis to follow it. Smith has very many fewer concrete examples than Reid. They are beautifully chosen classics, like Veronese maps and Segre maps, so they teach a lot. And the more you know to start with, the more you will see in each. The book does geometry over the complex numbers. It is good old conservative material, with terrific graphics of curves and surfaces. The proofs and partial proofs are very clear, intuitive and to the point. But, in fact, just because the proofs are so clear and to the point they usually work in a much broader setting. Long stretches of the book apply just as well over any field or any algebraically complete field. This generality is only mentioned a few times, in passing, but is there if you want it. Smith describes schemes very briefly, and mentions them at each point where they naturally arise. You will not know what schemes "are" at the end of this book. You will know some things they DO. She has no time for fights between "concretely complex" and "abstractly scheming" approaches--for her it is all geometry. ... Read more |
12. Real Algebraic Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Jacek Bochnak, Michel Coste, Marie-Francoise Roy | |
Paperback: 430
Pages
(2010-11-02)
list price: US$199.00 -- used & new: US$199.00 (price subject to change: see help) Asin: 364208429X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
13. Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series (Ergebnisse der Mathematik Und Ihrer Grenzgebiete) (Volume 0) by R.K. Lazarsfeld | |
Paperback: 387
Pages
(2004-08-24)
list price: US$34.95 -- used & new: US$28.56 (price subject to change: see help) Asin: 3540225285 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This two volume work on |
14. Complex Analysis and Algebraic Geometry: A Collection of Papers Dedicated to K. Kodaira | |
Paperback: 416
Pages
(2009-04-13)
list price: US$50.00 -- used & new: US$43.19 (price subject to change: see help) Asin: 0521093341 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
15. Rudiments of algebraic geometry (University texts in the mathematical sciences) by William Elliott Jenner | |
Paperback: 104
Pages
(1963)
Asin: B0006AYF2I Canada | United Kingdom | Germany | France | Japan | |
16. Algebraic and Analytic Geometry (London Mathematical Society Lecture Note Series) by Amnon Neeman | |
Paperback: 434
Pages
(2007-09-24)
list price: US$85.00 -- used & new: US$68.70 (price subject to change: see help) Asin: 0521709830 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
17. Principles of Algebraic Geometry by Phillip Griffiths, Joseph Harris | |
Paperback: 832
Pages
(1994-08-02)
list price: US$137.00 -- used & new: US$93.86 (price subject to change: see help) Asin: 0471050598 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
high five
A review from a graduate student 1. Complex Analysis Do not expect chapter 0, "Foundational Material", to be the place where you are supposed to build your "foundation". You can try the books of Michael Spivak, David A. Cox, Fangyang Zheng, among other books for foundational material but not chapter 0. However, if you have most of the above-mentioned foundational material, then this book is good in presenting complex manifolds for example in chapter 0 section 2 and also in presenting (complex) holomorphic vector bundles, as well as many other things. So, in summary, I would say a good book but not for students trying to learn the basics in algebraic geometry.
algebraic geometry: the real stuff
Work of Art
Absolutely indispensable |
18. The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics) by David Eisenbud | |
Paperback: 248
Pages
(2005-02-01)
list price: US$44.95 -- used & new: US$27.99 (price subject to change: see help) Asin: 0387222324 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, an appendix provides a summary of commutative algebra, tying together examples and major results from a wide range of topics. Customer Reviews (1)
Great book |
19. Algebraic Geometry: A First Course (Graduate Texts in Mathematics) by Joe Harris | |
Paperback: 328
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 144193099X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description "This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS Customer Reviews (4)
Not for a beginner
22 lectures = 5 stars
too many examples
Definitely a good start in algebraic geometry In lecture 1, the author introduces affine and projective varieties over algebraically closed fields. Linear subspaces of n-dimensional projective space P(n) are shown to be varieties, along with any finite subset of P(n). He delays giving rigorous definitions of degree and dimension, emphasizing instead concrete examples of varieties. The twisted cubic is given as the first example of a concrete variety that is not a hypersurface, along with their generalizations, the rational normal curves. The Zariski topology, considered by the newcomer to the subject as being a rather "strange" topology, is introduced in lecture 2. The author does a great job though explaining its properties, and introduces the regular functions on affine and projective varieties. The Nullstellensatz theorem, needed to prove that the ring of regular functions is the coordinate ring, is deferred to a later lecture. Rational normal curves are further generalized to Veronese maps in this lecture, and the properties of the corresponding Veronese varieties discussed in some detail. Also, the very interesting Segre varieties are discussed here. With these two examples of varieties, the reader already can develop a good geometric intution of the behavior of typical varieties. The Veronese and Segre maps are then combined to give another example of a variety: the rational normal scroll. More concrete examples of varieties are given in the next two lectures, including cones, quadrics, and projections. A "fiber bundle" approach to forming families of varieties parametrized by a given variety is outlined here also. The author finally gets down to more algebraic matters in lecture 5, with the Nullstellensatz proven in great detail. He also discusses the origins of schemes in algebraic geometry, giving the reader a better appreciation of just where these objects arise, namely the association to an arbitrary ideal, instead of merely a radical ideal. Grassmannian varieties are then introduced in lecture 6, along with some of its subvarieties, such as the Fano varieties. The join operation, widely used in geometric topology, is here defined for two varieties. More connections with the modern viewpoint are made in lecture 7, where rational functions and rational maps are discussed. The author takes great care in explaining in what sense rational maps can be thought of as maps in the "ordinary" sense, namely they must be thought of as equivalence classes of pairs, instead of acting on points. The very important concept of a birational isomorphism is discussed also, along with blow-ups and blow-downs of varieties. Many more concrete examples of varieties are given in lectures 8 and 9, such as secant varieties, flag manifolds, and determinantal varieties. In addition, algebraic groups on varieties are discussed in lecture 10, allowing one to discuss a kind of glueing operation on varieties, just as in geometric topology, namely by taking the quotient of varieties via finite groups. The author then moves on to giving a more rigorous formulation of dimension, giving several different definitions, all of these conforming to intuitive ideas on what the dimension of an algebraic variety should be, and also one compatible with a purely algebraic context. Again, several concrete examples are given to illustrate the actual calculation of the dimension of a variety, both in this lecture and the next one. The next lecture is very interesting and discusses an important problem in algebraic geometry, namely the determination of how many hypersurfaces of each degree contain a projective variety in P(n). The solution is given in terms of the famous Hilbert polynomial, which is determined for rational normal curves, Veronese varieties, and plane curves in this lecture. The author also explains the utility of using graded modules in the determination of the Hilbert polynomial, something that is usually glossed over in most books on this topic. This discussion leads to the Hilbert syzygy theorem. Some analogs of basic contructions in differential geometry are defined for varieties in the next four lectures, based on an appropriate notion of smoothness. The tangent spaces, the Gauss map, and duals discussed here. Then in lecture 18 the author makes good on his promise in earlier lectures of making the notion of the degree of a projective variety more rigorous. The well-known Bezout's theorem is proven, after introducting a notion of transversal intersection for varieties. As usual in the book, several examples are given for the calculation of the degree, including Veronese and Segre varieties, in this lecture and the next. The behavior of a variety at a singular point is studied in lecture 20 using tangent cones. The author proves the resolution of singularities for curves here also. Lecture 21 is very important, especially for the physicist reader working in string and M-theories, as the author introduces the concept of a moduli space. Most results are left unproven, but the intuition gained from reading this lecture is invaluable. The all-important Chow and Hilbert varieties are discussed here. The book the ends with a fairly lengthy overview of quadric hypersurfaces. ... Read more |
20. Basic Algebraic Geometry 2: Schemes and Complex Manifolds (Volume 0) by Igor R. Shafarevich | |
Paperback: 269
Pages
(1994-08-08)
list price: US$74.95 -- used & new: US$51.99 (price subject to change: see help) Asin: 3540575545 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 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. Customer Reviews (2)
Are you looking for literary criticism? It's a freaking math book!
Was the book modified without modifying the index? |
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