Rising Sea by Ravi Vakil - algebraic geometry

[rileylev]

This is the book people recommended me for learning Algebraic Geometry. The drafts are available on the author's website https://math.stanford.edu/~vakil/216blog/ . The writing is clear and conversational. There's lots of diagrams and discussion specifically about how (and why) to visualize schemes. It's a scheme-first approach.

"Wiser heads would counsel spending time understanding complex varieties in some detail before learning about schemes. Instead, I encourage you to learn about schemes immediately, learning about affine complex varieties as the central (but not exclusive) example. This is not ideal, but can save time, and is surprisingly workable" (Vakil 14).