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Kurzbeschreibung
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
Synopsis
A comprehensive, self--contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
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Einleitungssatz
In this chapter we sketch the foundational material from several complex variables, complex manifold theory, topology, and differential geometry that will be used in our study of algebraic geometry. Lesen Sie die erste Seite
Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
In this chapter we sketch the foundational material from several complex variables, complex manifold theory, topology, and differential geometry that will be used in our study of algebraic geometry. Lesen Sie die erste Seite
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Kundenrezensionen
Die hilfreichsten Kundenrezensionen
5 von 5 Kunden fanden die folgende Rezension hilfreich
Format:Gebundene Ausgabe
This book is a throwback to the time when algebraic geometry was a branch of geometry rather than category theory. As wonderful as the books by Mumford and Hartshorne are, they are rather long on abstract nonsense and short on geometry. This book is a refreshing exception to the 'modern' trend. Actually, there is a renaissance in applications of algebraic geometry to surprizing fields such as encryption and string field theory, and these are more in the spirit of this book than those of the Grothendieck school. Except for the obscenely high price and occasional typos, I highly recommend this book, especially to geometrically inclined mathematicians who don't really care about the category of schemes over an arbitrary field
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38 von 39 Kunden fanden die folgende Rezension hilfreich
The Book
16. Februar 2001
Format:Taschenbuch
Just wanted to add the following:
1) The mathematics in this book is some of the most beautiful stuff I've ever seen. I don't in any way mean to deny the beauty of the Spec of a Ring, but - even if you have always planned on working in Grothendeick's world - I think this is worth reading for any algebraic geometer (regardless of what field you're living over).
With their bare hands, Griffiths and Harris prove some of the greatest results in maths. I learned more reading Chapter O than I did taking the entire collection of "first- year" grad courses (algebra & analysis). The material was more interesting, and it tied together in a way that had you remember all of it. From elliptic operator theory to the representation of sl(2), in the same chapter!
2) For string theorists trying to learn some of the math lingo, this is a necessary first step, though I would also highly recommend Candelas's notes, and Aspinwall's great paper, "K3 Surfaces and String Duality". Also, Brian Greene's notes are very nice. T. Hubsch's book is also great for the big picture, but I was disappointed by several non-trivial errors in his explanations of math concepts. I recommend all of the above to mathematicians as well - I am a mathematician, and I learned a lot of valuable side material from these physics sources. Especially in trying to understand mirror symmetry. Of course, Cox and Katz's newish book is also excellent for this.
3) My favorite parts: chap 1: divisors and line bundles, the exp sheaf sequence. read this, and then skip to the same picture for line bundles on a torus. the same type of bouncing back and forth works for getting the analogs between Reimann surfaces and complex surfaces...
actually, every page of this huge book has something valuable. I can't imagine what it was like to learn this field before this book came along. The price is exorbitant, but in the grand scheme of things, I've spent hundreds (thousands?) on math books that lie on my shelf, never to be explored. this one has given me years of enjoyment.
43 von 48 Kunden fanden die folgende Rezension hilfreich
More geometry, less algebra.
13. August 1997
Format:Gebundene Ausgabe
This book is a throwback to the time when algebraic geometry was a branch of geometry rather than category theory. As wonderful as the books by Mumford and Hartshorne are, they are rather long on abstract nonsense and short on geometry. This book is a refreshing exception to the 'modern' trend. Actually, there is a renaissance in applications of algebraic geometry to surprizing fields such as encryption and string field theory, and these are more in the spirit of this book than those of the Grothendieck school. Except for the obscenely high price and occasional typos, I highly recommend this book, especially to geometrically inclined mathematicians who don't really care about the category of schemes over an arbitrary field
27 von 29 Kunden fanden die folgende Rezension hilfreich
A review from a graduate student
15. März 2004
Format:Gebundene Ausgabe
If you are a graduate student in mathematics or related fields and you are interested in learning algebraic geometry in the Griffiths-Harris way, then I suggest before buying this book to have a good background in the following:
1. Complex Analysis
2. Differential Geometry and calculus on manifolds
3. Homology-Cohomology Theory
4. Undergraduate Algebraic Geometry
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.
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