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
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Fall 2025
Chi Li
Course Description:
This is a first course in algebraic geometry. Emphasis will be on basic notion and examples. We will cover most of Shafarevich's book: Basic Algebraic Geometry I. If there is time, we will also talk about schemes, coherent sheaves.
Text:
Shafarevich, Basic Algebraic Geometry I (Varieties in Projective Space)
Prerequisites:
Linear Algebrac, Abstract algebra, Complex Analysis
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Spring 2024
Lev Borisov
Course Description:
This is a first course in algebraic geometry. Selection of topics will somewhat depend on the background and interests of the participants. At a minimum, I intend to talk about projective spaces, line bundles, vector bundles, blowup construction and Riemann-Roch theorems, with emphasis on examples. The language of schemes and sheaves might be introduced in passing, but will not be the focus of the course.
Text:
None. I will try to find appropriate online notes for some of the topics we will cover.
Prerequisites:
No firm prerequisites. Some knowledge of commutative algebra, differential geometry and/or complex analysis would help. If in doubt, ask the instructor.
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Spring 2022
Ian Coley
Course Description:
This course will not be diving straight into Hartshorne as students hold on for dear life. Rather, we will go deliberately through the first steps in understanding varieties in projective space (so our first definition will not be "A scheme is ..."). We will tackle some more of the classical topics like elliptic curves, hypersurfaces, Grassmannians, etc. with a more complete syllabus to be compiled based on students' need and research interests.
Text:
Shafarevich, Basic Algebraic Geometry I (Varieties in Projective Space)
Prerequisites:
A definite prerequisite is Math 551 or equivalent. Math 552 is useful as a pre- or co-requisite.
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Fall 2020 - Lev Borisov
Course Description:
Introduction to toric varieties. This will be a mixture between a topics and an introductory course in algebraic geometry. While some prior familiarity with schemes and/or differential geometry is useful, it is not required. We will cover affine toric varieties, projective spaces, fan construction, quotient singularities, resolutions of singularities, Picard group and other topics in toric geometry.
Text:
TBD
Prerequisites:
None. If unsure, contact instructor ().
Schedule of Sections:
16:640:535 Schedule of Classes