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I'm interesting in studying algebraic geometry (specifically either from Shafarevich or Hartshorne). Assuming a high school and basic college math education, what should be the topics and the order that I should study them to get there? Also, could you recommend books/online resources for each topic. Thanks!

PS - I apologize if this question does not fit the rules of the forum. I will modify it as required if it doesn't.

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  • $\begingroup$ What counts as a basic college math education? Some calculus and linear algebra, or a complete undergraduate degree program? $\endgroup$
    – Hoot
    Commented Dec 14, 2014 at 5:22
  • $\begingroup$ @Hoot - Calculus and linear algebra. $\endgroup$
    – Prahar
    Commented Dec 14, 2014 at 5:24

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  1. Basic abstract algebra from a book like Artin or Herstine.
  2. Basic Commutative Algebra (first two chapters of Atiyah MacDonald)
  3. More commutative Algebra and Start of reading in algebraic geometry (Atiyah MacDonald again or Eisenbud's commutative algebra for algebra and Fulton or Schaferavitch 1).
  4. The first beast: Harshorne. At this point you could read Schaferavitch 2 too and more Eisenbud.
  5. The second beast: Griffis and Harris

By the time you reach 5, probally before then, you will know which topics you are interested in and will be able to find the resources you need for yourself.

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    $\begingroup$ Correct spelling is: Herstein, Shafarevich (standard English transliteration), Hartshorne, Griffiths. $\endgroup$
    – Georges Elencwajg
    Commented Dec 14, 2014 at 10:20
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    $\begingroup$ Even trickier is the pronunciation of Hartshorne. $\endgroup$
    – Hoot
    Commented Dec 14, 2014 at 16:10
  • $\begingroup$ @ChrisDugale - Thanks! This helps a lot. $\endgroup$
    – Prahar
    Commented Dec 15, 2014 at 16:52

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