I plan to self-learn Algebraic Geometry. I have an undergraduate degree in Math. I cannot find a clear answer on what the clear textbook could be. There are also some notes online on the subject, like Gathmann and Milne.
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2For scheme theory I personally like Liu's book, it includes all the necessary background in commutative algebra if you know the basics on rings and modules. – Wojowu Nov 22 '19 at 18:22
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3check out this MO post: https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne – d_b Nov 22 '19 at 18:22
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May I suggest not trying to do that alone? Algebraic geometry is hard, and I’ve found that you really need to work through any text on the subject. So if you can study with someone, or even attend some lectures, I think it’s going to be very helpful. – Aphelli Nov 22 '19 at 18:35
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Is there any online lectures you recommend? – Sinewaveman Nov 22 '19 at 18:37
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I’m sorry, I don’t know of any. – Aphelli Nov 22 '19 at 18:43
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@Wojowu do you mean Qing Liu ? Or is it someone else ? – user577215664 Nov 22 '19 at 18:43
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1@Isham That's the one – Wojowu Nov 22 '19 at 18:43
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Thanks a lot @Wojowu ..... – user577215664 Nov 22 '19 at 18:45
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There's a book in the TRIM series by C. Musili called Algebraic Geometry for Beginners. That might be a good place to start. – Siddharth Acharya Nov 22 '19 at 19:57
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The fact that you have undergraduate degree does not tell us much. What kind of courses have you taken in Algebra/Topology/Geometry area. What topics have you covered? – Mihail Nov 23 '19 at 01:12
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One problem with the subject is that one can lose the forest for the trees when learning the foundations. It's good to have a motivating, geometric goal, even though the foundations are interesting.
One route: Learn algebraic curves and Riemann surfaces first (Miranda's book is good if you are aiming for geometry, or Silverman's first GTM on Elliptic Curves if you are aiming for number theory, or both). Then learn foundations with Hartshorne or Vakil's notes or EGA or what have you.
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As said above Miranda's book is a great starting resource and it contains very advanced topics too, it starts in the world of complex geometry as manifolds and ends with algebraic varieties. I would also suggest Igor R. Shafarevich's Basic Algebraic Geometry 1 too.
For a more consice book there is also ALGEBRAIC CURVES: An Introduction to Algebraic Geometry by William Fulton which contains plenty exercises and is on the more algebraic side of things.
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