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Lifted from Mathoverflow:

I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best. Then what might be the 2nd best? It can be a book, preprint, online lecture note, webpage, etc.

One suggestion per answer please. Also, please include an explanation of why you like the book, or what makes it unique or useful.

  • 3
    Since from my point of view the subject is too broad to choose only one book, I posted an answer with my choices for "best book" depending on the focus one is approaching algebraic geometry... Hope that is ok, if not, I shall remove it.2011-03-01

10 Answers 10