algebraic geometry...where to begin?

[styler]

Howdy folks,
I was wondering if anybody could recommend a good place to start learning algebraic geometry as might be relevant for current/recent mathematical physics.
I have opened Griffiths and Harris and found it sprawling ad frustruating.
For the sake of judging what might be appropriate, i am mainly interested in physics but i have completed stadarnd first year math course work in topology, algebra and analysis and additionally taken courses in functional analysis, differnetial topology, differetial geometry and alebraic topology...so i guess i "know" about what a very modest begining third year grad student in math has learned.
Recomedations for several complex variables would be appreciated as well.
Any ideas?
Thanks in advance.

[Hurkyl]

Others suggested these texts for me:

Basic Algebraic Geometry - Shafarevich
Algebraic Curves - Fulton
Algebraic Geometry - Hartshorne

And I've found them useful so far. If you just wanted to look at one, I'd probably suggest Shafarevich.

Keep in mind that I've just started teaching myself the subject, so I'm by no means an expert on the available choices. :smile:

[styler]

cool. thanks. I have heard about the first one...how elemetary/advanced is it?

[Hurkyl]

It starts off, IMHO, fairly elementary. (admittedly, "elementary" is a relative term!) The later chapters go into schemes and are fairly more advanced, but Shafarevich is still nowhere near as difficult as Hartshorne. (I haven't peeked at the Complex Manifold chapters in Shafarevich, though)

[phoenixthoth]

hartshorne has as a precursor commutative algebra by eisenbud.

an intro alg. geometry book is rings varieties and algorithms by cox, little, and o'shea. it's prolly a good thing to have as a companion when looking at real alg. geometry.

[styler]

thanks guys
maybe i'll post some questiogs as i go alog.