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I had taken course in complex analysis and self-studied differential manifolds and basic topology from Loring Tu Introduction to Manifold. What else do I need (minimally) to prepare myself to read the Principal of Algebraic Geometry by Philip Griffiths? (Do I need Huybrechts Complex Geometry or Rick Miranda's Algebraic curve and Riemann surface?)

Nothing
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    Prepare to encounter many typos and errors in the book.....But now you can find a (but not complete) list of errors in here: https://mathoverflow.net/questions/13000/errata-to-principles-of-algebraic-geometry-by-griffiths-and-harris – Tony Jun 05 '20 at 12:14
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    @Tony , is my background enough? – Nothing Jun 05 '20 at 12:17
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    I have pages and pages of errata, but I haven't thought about them in 35+ years and I am not prepared to add them to lists. I would say that Huybrechts is somewhat parallel (but far less comprehensive). You need some algebraic topology and differential geometry — definite comfort with basic homology and cohomology, differential forms, and connections on vector bundles. Learning the background from Chapter 0 is not advisable. – Ted Shifrin Jun 07 '20 at 03:35

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Also too long for a comment. So I too will put it as an answer.

  1. I was told in a comment to one of my deleted questions that Griffiths' Introduction to Algebraic Curves is a prerequisite to griffiths harris principles of algebraic geometry.

  2. I used Rick Miranda's Algebraic curve and Riemann surface (chapters I - VIII) as an alternative to Griffiths' Introduction to Algebraic Curves.

  3. It appears that griffiths harris principles of algebraic geometry somewhat overlaps with both Rick Miranda's Algebraic curve and Riemann surface (chapters IX onwards) and Huybrechts Complex Geometry.

P.S. I actually have to study Griffiths' Introduction to Algebraic Curves, Huybrechts Complex Geometry and chapters 0 and 1 of griffiths harris principles of algebraic geometry, and I'm hoping it will suffice to study Rick Miranda's Algebraic curve and Riemann surface (chapters I - VIII), chapters 0 and 1 of griffiths harris principles of algebraic geometry and all the complexification I studied in external sources (see my questions eg this one or this one)

BCLC
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It's too long for a comment. So I will put it as an answer. First, sorry for my above (maybe sarcastic) comment. I had painful time reading Griffiths and Harris thanks to the many typos and errors in the book. As you may have already known, there are quite a lot of typos in the book which makes it hard to read. However, as I have pointed out, you may find this list helpful. Other than the errors, I think Griffiths and Harris is a good book.

Let me go back to your question. To answer your question, I think it really depends on your goal: Do you want to finish reading the whole book? Or do you want to read, say, the first two chapters of the book? Frankly, I myself did not finish reading the whole book. I finished reading chapters 0 and 1, and first few sections of chapter 2. If you also have some knowledge in complex analysis, then I would say that you, with the background knowledge of manifold theory and topology, will have no problem reading the chapters 0 and 1.

Tony
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    Do I need Riemannian geometry and characteristic class to study the chapters other than Chapter 0,1 and 2? – Nothing Jun 05 '20 at 12:46