Algebraic Geometry (Graduate Texts in Mathematics, 52) by Robin Hartshorne (PDF)

Description

Note: Item do have Large Margins. An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of “Residues and Duality”, “Foundations of Projective Geometry”, “Ample Subvarieties of Algebraic Varieties”, and numerous research titles.

User’s Reviews

Editorial Reviews: Review R. HartshorneAlgebraic Geometry”Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions.”―MATHEMATICAL REVIEWS About the Author

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This might be one of the most difficult books on the subject matter, and is definitely the most difficult book I read, but if you put in the hard work into it, do all the exercises, you will learn a lot from it. One really cannot blame Hartshorne for the difficulty of this book. Algebraic geometry is a hard topic that requires a large list of prerequistes. If you want to learn algebraic geometry on the level of actual mathematicians then there is no way around the topics in this book. Hartshorne made it possible for the rest of the mathematical community to actually learn this topic, which before him was highly inaccessible.The disadvantage is that much motivation is non-existent. However, if you learn the vocabulary and basic theorems of this topic, then you can try to look for motivations else where. Perhaps, this is a backwarks way of learning the subject but it is very direct and to the point. The advantage is that this book slaps you over the face with all the technical stuff. It is not wordy and to the point.The exercises are helpful and I learned way more from them than reading the actual text. Perhaps a possible compromise to Hartshorne is to learn AG from other sources and then do all of his exercises.I do wish that Hartshorne did a better job on Chapter 1. It is not necessary for the remainder of the text but it helps develop intuition. A problem with Hartshorne’s approach is that he defines varieties living in some affine space. This is a bit annoying, he should have defined them with reference to an ambient space (just like the definition of “manifolds” in differential geometry, no reference to an ambient space). I think this would have made the introduction of sheaves more natural.Just a disclaimer. Make sure your basic algebra is solid, especially commutative algebra, and be well-versed in point-set topology.

⭐algebraic geometers are really bad at pedagogy.

⭐Hartshorne is a great book. Brutal, but insightful.In my experience, the newer copies of the yellow bois come with varying levels of binding quality (ranging from embarrassing to passable). This copy of Hartshorne has the best binding that I’ve gotten from one so far (much better than my copy of Conway, which almost survived through a one-semester course!).

⭐Hartshorne remains the standard for diving into the field of algebraic geometry. But the copies I, and several others I know who bought the book from Amazon, got very poor quality copies. Compared to the copy my library has, the printing is blurry, the paper feels cheap, and the book can’t hold itself open. If you’re going to be seriously studying this book, you’ll probably spend several months carrying it around. In this case, the binding is likely to fall apart. One person in my department even got a copy printed with margins so wide that the text filled less than half the page. (On a related note, someone else ordered another Springer text and ended up with a book with the correct cover, but an entirely different, unrelated text, inside. Fortunately, that was hilarious.)I’m not sure where you can get a better quality copy nowadays. If you find one, it’s worth an extra expense over one that will just disintegrate.

⭐This review is about the copy I received from Amazon. The quality of print is not good. The printing is not sharp and you can see tiny black dots all over the page in all the pages. I didn’t notice it first and it’s not too bad but not something that I expected for costly textbooks.

⭐Algebraic Geometry Bible

⭐must have

⭐Great book

⭐Well printed and still the best book to learn schemes and sheaf cohomology through its exercices.

⭐Un très bon livre pour les géomètres. Qualité très bien, lisible. C’est un peu cher, mais vu que c’est pour une utilisation à vie, je pense que ça mérite.Achat parfait !Très bonne ouvrage de surcroît !相場よりとても安くて、中身もとても綺麗で満足です。書いてある通り色褪せている部分もありましたが問題ないです。多くの数学者に推薦される本であり、じっくり読ませて戴きます。古典的扱いから、スキーム論への展開が楽しみです。

⭐

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