Algebraic geometry #

Self-study curriculum #

My notes are here.

Algebraic geometry references #

  • Fulton - Algebraic Curves
  • Hartshorne - Algebraic Geometry (GTM 52)
  • Holdener - CMU Notes
  • Kirwan - Complex Algebraic Curves (LMS 23)
  • Vakil - The Rising Sea

Commutative algebra references #

  • Atiyah-McDonald - Introduction to Commutative Algebra
  • Clark - Commutative Algebra
  • Eisenbud - Commutative Algebra (with a view to Algebraic Geometry) (GTM 150)
  • Matsumara - Commutative Algebra
  • Nelson - Notes on Krull Dimension
  • The Stacks Project, an open-source textbook / knowledge repository on algebraic geometry, up to algebraic stacks and their theory. Cool idea, but I found it extremely terse.
  • A nice post on how memory constructs in Minecraft can be thought of as sheaves.
  • Some great notes on algebraic geometry from an introductory course at Cornell.
  • A nice textbook freely available online about algebraic curves (i.e. one-dimensional algebraic geometry) by William Fulton.
  • Some more great notes from an introductory course at TU Kaiserslautern.
  • Notes on abelian varieties by Bhargav Bhatt.
  • A nice textbook called “Sheaf Theory through examples”
  • Some nice lecture notes that start from basic motivating examples.
  • A really great video course by Miles Reid with 32 lectures on YouTube.
  • Another 36-lecture video course by Ben Webster available from the Fields Academy.