Instructor: Andrew Hanlon

About: In this course, we will study toric varieties. Due to their large amount of symmetry, toric varieties are particularly amenable to characterization and computation. As such, they provide a rich class of examples and serve as a fertile testing ground for more general theorems. We will work with these varieties mostly in the realm of algebraic geometry. For example, we will study their divisors, line bundles, and sheaf cohomology. Along the way, we may also take a detour into the symplectic geometry of toric varieties.

Prerequisite: You should be comfortable with graduate level algebra (e.g., MAT 534 and 535) and topology (e.g., MAT 530 and some of 531). You should also have some background in algebraic geometry (e.g., MAT 589) although toric varieties provide a great way to shore up your algebraic geometry knowledge or build on a smaller foundation.

Office Hours: Mondays 11:30 am - 12:30 pm and Thursdays 2 - 3 pm in 304 Simons Center for Geometry and Physics (if you would prefer to meet on Zoom, please contact me in advance).

Math Learning Center Hours: Thursdays 9-10 am via Zoom and accessed from the MLC website.

Lectures: Mondays and Wednesdays 9:45-11:05 am in Physics P-130.

Syllabus: The course syllabus is available here.

Main Textbook: D. Cox, J. Little, and H. Schenck, Toric Varieties

Additional Resources:

• W. Fulton, Introduction to Toric Varieties

• F. Sottile, Ibadan Lectures on Toric Varieties

• J.-P. Brasselet, Introducton to Toric Varieties

• A. Cannas da Silva, Symplectic Toric Manifolds

Note: As this is a graduate course, you won't be assigned many exercises (see the syllabus above). However, if you want to really learn the material, I recommend regularly doing exercises from the book by Cox, Little, and Schenck or another source. I would be happy to discuss your solutions or ideas.