Fall 2026
Anders Buch
Course Description:
Algebraic Geometry is the study of geometric figures cut out by polynomial equations. Such figures can be studied using a mixture of algebraic and geometric methods. A central theme of the subject is that problems can be translated back and forth between algebraic and geometric viewpoints. The main goal of the course will be to develop the beautiful theory of algebraic varieties over an algebraically closed field. Topics will include affine, projective, and complete varieties, products of varieties, dimension, rational maps, non-singular varieties, divisors and line bundles, coherent sheaves, algebraic curves, and the Riemann-Roch theorem. At some point we will introduce
schemes, which makes it possible to assign geometry to any commutative ring.
Text:
Hartshorne: Algebraic Geometry / Vakil: The Rising Sea (the books will not be followed closely)
Prerequisites:
16:640:551
Schedule of Sections:
16:640:535 Schedule of Classes
Previous Semesters
- Fall 2026 - Buch, Anders
- Fall 2025 - Li, Chi
- Spring 2024 - Borisov, Lev
- Spring 2022 - Coley, Ian
- Fall 2020 Prof. Borisov
- Fall 2019 Prof. Gibney
- Fall 2016
- Fall 2008
- Fall 2002