Algebraic Geometry

This page serves as a compilation of the main takeaways of various topics in classical algebraic geometry. In particular, the following discussions and remarks are to make clear the ideas and wholistic understanding of mathematics. One of the most important things to do in math is to understand the insight that a theorem or technique can provide in your larger understanding of the field. This is what I have attempted to do here to the best of my ability.

Within each section I choose to omit certain proofs, whose proof techniques seem to "get in the way" of the main takeaways. When this is done there will be a link to a proof in the "proofs of the trade tab".

The main references for this are "An Invitation to Algebraic Geometry" by Karen Smith, Lauri Kahanpaa, Pekka Kekalainen, and William Traves and "Algebraic Geometry" by Robin Hartshorne.