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My question is a short one, but hopely I get long answers...I am looking for bibliography on Algebraic Geometry. A first but complete book, rigorous and also modern. I want to say that Hartshorne`s is great to me, it covers a graet range of topics, it gives some paths to pursue the studies, and it fulfills all the mentioned requirements... I hope this book or books do exist, but may be I would need an explained interaction with Complex Geometry, for instance, to get a better flavour of abstract notions. I mention Complex Geometry, but many approaches other than those used by H. would really help. I really want to see Algebraic Geometry immersed in the rest of mathematics, But I lack the knowledge to do so. Anyway, it is Algebraic Geometry I am intested in, so it is a different FLAVOUR I am (just) looking for!

vanmeri
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    See here, here and here. – Krish Nov 24 '18 at 15:10
  • Hartshorne is the best book in A.G. I know that is awfully terrible for beginners. One must be very careful when trying to study from scratch with books like this one: they can be depressing. – DonAntonio Nov 24 '18 at 15:27
  • Now I do have material!!It is a jungle so vast that learning to choose from there is already learning A.Geometry!!That is good...I see I am not the only one with the same "problem". Better still, so that I may compare my conclusions on bibliography from time to time...Thanks for the answer. – vanmeri Nov 24 '18 at 15:29

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Hartshorne is the best you can get. I'd look into the manuscripts of Gathmann that you will find at the Internet as PDFs. These texts are stringent and contain some motivation for the reader.

Wuestenfux
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