I've been trying to learn some algebraic geometry (level of generality: working over an algebraically closed ground field but not afraid of using the language of sheaves and cohomology etc.)
The problem I'm having with it is that most of the references I'm using (Milne's notes on AG, Perrin's Algebraic Geometry, Mumford's Red Book etc.) just seem like endless streams of technical results and whilst I can appreciate most of the concrete examples ("oh look - that's a singularity"...), I'm not really sure what I'm supposed to be doing. On the other hand, books like Reid's Undergraduate AG makes me feel like I'm not sure what the definitions are (if that makes sense to someone!).
At the minute my approach is to check everything line by line (if I can!) and try to build up a picture of how the technicalities fit together into a bigger picture. I've also tried to do the exercises in Chapter 1 of Hartshorne but a lot of them seem too difficult for me at the moment (there feels a big gap between the technicalities of the chapters in the books and the concrete nature of the examples).
Does anyone have some magical book recommendation that I've missed or some other approach that helped them learn the subject?
Many thanks!