Introduction

This page will cover, hopefully completely, my journey through the vast field of algebraic geometry via Hartshorne's text. Most of the posts here will consist of solutions to the hundreds of exercises proposed in the book, but occasionally if an insight, question, or interesting problem strikes my eye I may write an expository post discussing the concept. By the time I am finished, I hope to have a full set of solutions in this repository for others to use in the future. I feel no need to write a longer introductory post, so I will simply cover my basic notions here before moving on.

Post Structure. Each exercise-based post will contain exactly one exercise. If the exercise is divided into multiple parts a), b), c), et cetera, all parts will appear in one post. The title will consist of the chapter number, the exercise number, and a brief 3-10 word summary of the idea of the problem (sometimes provided by Hartshorne, mostly not). For example, the post corresponding to the book's third exercise would be Chapter 1, Exercise 1.3: A Multi-Component Algebraic Set. Within the post will first be a statement of the problem, and then the solution divided into lemmas and the final proof as is necessary.

Expository posts will be labeled as such. For example, a post on properties of graded rings would be titled Expository: Properties of Graded Rings or similar. Such posts will consist of nothing more than the discussion involved.

Starred Exercises. For the most part, I will attempt to complete exercises in order, doing each one without stopping and using only techniques discussed in the book up to the given point. However, in the special case of exercises that have been starred as difficult I may skip them, creating a post with no solution and come back to them later, perhaps with more tools at my disposal.

Double-Starred Exercises. Double-starred exercises correspond to open problems in the world of Hartshorne. I will create a post for each such exercise and either write a brief commentary on the problem or simply mention that it is a double-starred and thus open problem.

Thanks for stopping by!