- Tapa dura: 496 páginas
- Editor: Springer; Edición: 1st ed. 1977. Corr. 8th printing 1997 (1 de abril de 1997)
- Colección: Graduate Texts in Mathematics
- Idioma: Inglés
- ISBN-10: 0387902449
- ISBN-13: 978-0387902449
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº132.008 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
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Algebraic Geometry (Graduate Texts in Mathematics) (Inglés) Tapa dura – 1 abr 1997
Descripción del producto
"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
Reseña del editor
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.
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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.
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.