These are notes on Algebraic Geometry. I plan to loosely follow the structure of Hartshorne’s Algebraic Geometry, filling in some details when necessary. I’ll also suppliment with Vakil’s The Rising Sea and other texts as needed. I’m following a rather depth-first approach with these notes, so LARGE sections will remain incomplete for a long time.
On Blowing Up a Sheaf of Ideals
Let be a scheme of finite type over a field . First we work with the affine case, so be an affine scheme. We assume for ease that .