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I liked using Rick Miranda's Algebraic Curves and Riemann Surfaces chapters I to VIII as an alternative to Griffiths' Introduction to Algebraic Curves. I notice they overlap in most topics.

I notice Rick Miranda's Algebraic Curves and Riemann Surfaces IX onwards overlaps with Griffiths Harris "Principles of algebraic geometry" chapters 0 and 1, but not really for most topics.

What are some alternatives to Griffiths Harris "Principles of algebraic geometry" chapters 0 and 1 that preferably are like Rick Miranda's Algebraic Curves and Riemann Surfaces chapters I to VIII as an alternative to Griffiths' Introduction to Algebraic Curves?

Here's a screenshot of the table of contents for Griffiths Harris "Principles of algebraic geometry" chapters 0 and 1

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P.S. Not sure if this relevant, but: 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.

Edit: Maybe related:

What to study after Miranda's "Algebraic curves and Riemann surfaces"?

What do I need to read Philip Griffths

Jean Marie
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BCLC
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1 Answers1

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I think pretty much everything you need is in Huybrechts' book titled Complex Geometry. This has the benefit of having many exercises and being written for someone new to the subject, whereas I think that Griffiths and Harris assumes that you already have had exposure to the materials in chapter $0$.

The book is available through Springer.

Alekos Robotis
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  • well i did start with Huybrechts' Complex Geometry before even miranda (see my previous questions on complexification eg https://math.stackexchange.com/questions/3520787/f-is-the-complexification-of-a-map-if-f-commutes-with-almost-complex-structu) but got stuck on complexification. good to know i can use huybrechts as an alternative. thanks! – BCLC Oct 31 '20 at 06:55
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    Did huybrecht have a self contained chapter on Hodge theory? – Arctic Char Oct 31 '20 at 07:09
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    Huybrechts does discuss Hodge theory in some level of detail. Like most introductory books on the subject, he doesn't get too far into the analytic aspect of the subject. – Alekos Robotis Oct 31 '20 at 15:30
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    @JohnSmithKyon if you've read most of Miranda since you last looked at Huybrechts, you will probably find it much easier going now that you have studied much of the $1$-dimensional theory. Although I don't think he covers Grassmannians, for which you might want to just bite the bullet and read Griffiths-Harris (or some of Harris' more recent expositions, such as in Algebraic Geometry: A First Course or 3264 and All That (the latter joint with Eisenbud). – Tabes Bridges Oct 31 '20 at 22:10
  • Alekos Robotis , i think you have to tag like this @ArcticChar. thanks Alekos Robotis and ArcticChar! – BCLC Nov 03 '20 at 14:21