17
$\begingroup$

I need to learn about Algebraic Geometry (perhaps from in the context of finite fields) and am looking for a recommendation for a text. Now, I've already done a search and checked out what was suggested. However, they weren't what I was looking for. To be honest, I felt that the suggested textbooks were terrible. (This even included some famous ones like Hartshorne.) They all followed the format of Theorem - Proof - Theorem - Proof - etc... Although this format makes for a good reference, it has no educational value for me; in the end, I will know how to prove some specialised set of theorems but not understand what any of it really means or why anybody cares in the first place. So, I would like to focus more about the motivation and history of the field and its concepts in order to get a big-picture understanding. (I will worry about the fine technical details on my own.)

Does anyone know of such a book? I really appreciate your help!

  • 12
    Have you looked at Shafarevich? He provides a lot more motivation than Hartshorne. Also, after you have read som AG, Eisenbud and Harris' "The Geometry of Schemes" is wonderful.2012-07-23
  • 3
    Did you look at [Ravi Vakil's notes](http://math.stanford.edu/~vakil/216blog/)? More or less every algebraic geometry textbook that I know about has been listed in one of the questions you probably found; you're going to have to find one that works for you, and unfortunately it's going to be hard for someone to say which one that will be.2012-07-23
  • 7
    And I second the recommendation of Shafarevich. Miles Reid, who translated the book, says in the preface “My experience is that some graduate students can work hard for a year or two on Chapters II–III of Hartshorne and still know more or less nothing at the end of it.” So certainly their hearts are in the right place. It would also help to know what it is you want to learn and for what purpose. Algebraic geometry is gigantic.2012-07-23
  • 3
    I think it's definitely worth taking a look at Gathmann's notes (mentioned by Joachim below). While I have not studied them, I do have them saved to use in the future. There is a fair amount of discussion, the first chapter is solely motivational, and overall it seems quite pleasant. Here's the link: http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf2012-07-24
  • 0
    @Dylan I'm also a big fan of Vakil's notes and are monitoring thier development closely-but I think these notes are way too difficult and abstract for the questioner's purposes.2012-07-24
  • 0
    Thanks for the comments, guys. Just to put in some background (which I also commented on below): I'm trying to study algebraic coding theory, so I require some background in algebraic geometry. I'm in the process of obtaining a copy of Shafarevich and Reid now!2012-07-25

6 Answers 6