I'm not sure if this is an appropriate question in this forum, but here is the situation.
I must begin by saying that I know basically nothing about Algebraic Geometry, but this semester I will be doing a reading course in Algebraic Geometry.
Of course, I will be discussing the choice of a book with my instructor, however, I wanted to have a better idea when it comes to selecting a book.
So far, I have thought of the following books:
- Basic Algebraic Geometry, volume 1, by Shafarevich;
- Algebraic Geometry, by Hartshorne;
- Algebraic Geometry, a first course, by Joe Harris;
- A Royal Road to Algebraic Geometry, Holme etc.
So, I guess my first question is, since there are a few branches of Algebraic Geometry, why would a person select one of these books over the others? Second, which of these books(or others that I don't know about),in your opinion, is the best book for someone who is just beginning to learn about Algebraic Geometry.
My background goes up to a course in Commutative Algebra (Atiyah MacDonald).
My goal is eventually to do a PhD thesis in Algebraic Geometry (I am a first year graduate student). Thanks!