I am now using Fulton's book Algebraic Curves to learn algebraic geometry from and have just finished chapter 2. However I feel that the problems are not very inspiring (at the moment at least) and lack some depth. Where is a good source of problems in algebraic geometry that I can find at least at the level of Fulton?
I don't mind if people recommend specific problems from Hartshorne say as long as I can do them with the tools I have from Fulton. To be more specific, the next chapter of Fulton is on local properties of plane curves and computing intersection numbers, so if one can recommend problems for these, it would be good.
Thanks.
Best Answer
Thomas A. Garrity has led a remarkable project aiming at teaching elementary algebraic geometry by means of problems.
Definitions are given but there are no proofs. The readers, meticulously guided by a progression of exercises which constitute the heart of the course, should find the proofs by themselves: the Moore method in all its splendour!
The level is more elementary than Fulton's.
This project has very recently become the AMS book Algebraic Geometry: A Problem Solving Approach.
I haven't seen that book, but I believe that my first link above is to the manuscript used for the published book.