Possible Duplicate:
(undergraduate) Algebraic Geometry Textbook Recomendations
I am interested in algebraic number theory and I am recently acquainted with the theory of valuations, which further leads to Riemann-Roch theory, and which is closely related to algebraic geometry, and the algebraic-K-theory.
Therefore, my problem is:
Are there excellent introductory books of the theory of Algebraic Geometry to recommend?
Since I know in general nothing about this theory, I may want a book which explains the ideas as clear as possible and which at the mean time contains as much material as possible.
If I am asking too much, then any good book in your view suffices.
Thanks very much.
As I mentioned at another post Teaching myself differential topology and differential geometry
If you are interested in learning Algebraic Geometry I recommend the books of my Amazon list. They are in recommended order to learn from the beginning by yourself:
http://www.amazon.com/lm/RHQS8Y3V7LJRQ/ref=cm_pdp_lm_title_1
In particular, from that list, a quick path to understand basic Algebraic Geometry would be to read Bertrametti et al. "Lectures on Curves, Surfaces and Projective Varieties", Shafarevich's "Basic Algebraic Geometry" vol. 1, 2 and Perrin's "Algebraic Geometry an Introduction". But then you are entering the world of abstract algebra.
There is no a single complete book and much less explaining the ideas as clearly as possible. If you are starting from the very beginnig, I recommend these in this order: Karen Smith's, Beltrametti, Hulek, Safarechiv vol. 1, Perrin, Shafarevich vol. 2 and then scheme theory with Ueno's three volumes.... then you can jump with enough background to the bible by Hartshorne, or Griffiths/Harris for the more complex geometric side.