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I want to learn Algebraic geometry. My main focus will be on Varieties.

Can you recommend a good textbook for Algebraic geometry for a beginner?

jasmine
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    Please see Algebraic Geometry Text Recommendation. – N. F. Taussig Feb 24 '24 at 12:32
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    I will suggest Fulton's Algebraic Curves. I found it easy to follow as a beginner. It's good one to establish basic ideas. – Tony Pizza Feb 24 '24 at 13:03
  • @rschwieb I've posted an answer to this question instead of the much older question with a different emphasis linked in the comment above. With Beginning in Algebraic Geometry just having come out in 2025, I think it's an appropriate place to post about it, as it fits the question quite well. – J W Jun 19 '25 at 14:11
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    @JW If it's a good recommendation, it probably belongs on one of the umpteen older recommendation posts, explaining its strengths. Then you could point a link from the comments here to there. Spreading recommendations out thinly among lots of posts seems like it makes the information harder to find. – rschwieb Jun 19 '25 at 14:13
  • @rschwieb This question may be similar, and could do with a bit more detail, but I don't feel it's an exact duplicate. – J W Jun 19 '25 at 14:14
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    @rschwieb I see your point. On the other hand, a recommendation like this could easily get lost amongst the numerous older recommendations written long before a book with this relatively low entry level existed. Just my opinion. – J W Jun 19 '25 at 14:17
  • @JW Requiring exact duplication would rob the feature of most of what is good about it. The point of duplication links is to get the existing body of posts to cohere so that people can find stuff. You are right that the one link above isn't that great. But if the question does get closed as a duplicate, we can add many more such links. Among them all is already a wealth of information that more than covers the actual question here. – rschwieb Jun 19 '25 at 14:18
  • @rschwieb Fair enough. I will await the fate of this question. If it's closed as a duplicate, I can always add my answer to a sufficiently similar older question. – J W Jun 19 '25 at 14:23
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    @rschwieb Done. Hope it will make the answer easier to find along with alternatives. – J W Jun 19 '25 at 21:13

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[This reply may be too late for the original poster, but could help others coming across the question.]

There's an open-access book that came out very recently: Beginning in Algebraic Geometry by Clader & Ross, Springer 2025. Unlike some introductory algebraic geometry books that expect background in commutative algebra and topology, this one assumes only linear algebra and a basic introduction to rings, such as one would encounter in an undergraduate abstract algebra course. The requisite parts of commutative algebra and topology are introduced as the book proceeds and there's an initial chapter on polynomial rings to refresh or supply what's needed to go on to affine varieties in the chapters that follow. The book also introduces projective and quasiprojective varieties but stops short of scheme theory, instead providing a "coda" to give a brief taste of further topics and recommend some other references for further reading. I've only skimmed through the book so far but it looks quite nice and friendly. And since it's open access, anyone can just check it out for themselves.

J W
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    The digital book is neat. The "learning objectives" sections are something I appreciate that modern elementary school texts do better than classic texts :). There's also these "check for updates" links... neat feature. – rschwieb Jun 19 '25 at 14:22
  • @rschwieb I think most recent Springer digital books have the "check for updates" feature. – J W Jun 19 '25 at 14:54