Math 232AR: Introduction to Algebraic Geometry I (Harvard, Fall Semester 2024/25)

Meets: Every Monday and Wednesday, 3-4:15PM at Science Center 304

Office hours: TBD

Brief course description: This is an introductory course to schemes in algebraic geometry. The goal of the course is to get you sufficiently familiar with the language of schemes, so that you can pursue further courses/reading in algebraic geometry.

Some of the major topics that I am hoping to cover include: basic properties of schemes and of morphisms between schemes, fibered products and base change, quasi-coherent/coherent sheaves, line bundles, divisors, morphisms to projective space, relative Spec and Proj construction, blow-ups, resolution of indeterminacies, and finally if time permits, differentials.

(This list is not final and will be finalized as the semester progresses.)

Prerequisites: A good background in commutative algebra. Some background in varieties will be desirable, but not necessary.

Texts: I will not strictly follow one book, but I intend to mostly use the following references (which I have found useful over the years):

[Vak] Ravi Vakil, "The Rising Sea: Foundations of Algebraic Geometry".

[GW] Ulrich Görtz & Torsten Wedhorn, "Algebraic Geometry I: Schemes, with Examples and Exercises".

[Hart] Robin Hartshorne, "Algebraic Geometry".

Evaluation: Will be fully based on homework sets. One homework set will be issued every two weeks, with the first homework issued on Wednesday, September 11.