Which Book Best Covers Algebraic Geometry for String Theory?

[eok20]

I hope this is the right forum for this question. Over the summer I would like to rigorously study the type of algebraic geometry that plays a role in things like string theory. My mathematics background is that I just completed the first year grad sequence (differential topology, algebraic topology, lots of algebra, real and complex analysis). I am thinking of going through some of Griffiths and Harris's Principles of Algebraic Geometry: does this cover most of the relevant material? One problem with it (besides its difficulty) is that it has no exercises. Is there a similar book with problems or are there related problems I can find online somewhere?

Thanks!

 

[Bourbaki1123]

There are other books, the only one I know of that isn't way more to the pure side than that text is Ideas, Varieties and Algorithms, but it goes into the more computer science/robotics applications and so it is more discrete even than normal and most of the proofs are constructive.

Robin Hartshorne's text is sort of standard. It delves much more deeply into theoretical architecture of cohomology and schemes than your book appears to. It has problem sets, but many of them are very difficult and I don't think any of them are application problems nor do I recall much on applications being addressed.

 

[ice109]

there's a book by shafarevitch that's supposedly good but i haven't read it so i can't speak from experience.