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.