Toric Geometry Learning Seminar Spring 2023

Welcome to the seminar page for the Spring 2023 toric varieties learning seminar. We meet on Fridays in PMA 12.166 from 12:00 - 13:00. In the first ten weeks, we plan to cover almost all of Fulton's Introduction to Toric Varieties supplemented by Cox, Little and Schneck's Toric Varieties. The final four to five weeks are reserved for special topics, chosen by the participants.

• Sign-up for talks here.

Notes

• 2023-02-20: Week 3: The Orbit Cone Correspondence
• 2023-02-09: Week 2: Local Properties (DRAFT)
• 2023-01-30: Week 1: Cones, fans and toric varieties (DRAFT)
• 2023-01-09: Week 0. The briefest primer on algebraic geometry

Schedule Outline (Subject to Change)

• Weeks 1-2, Chapter 1: Cones, fans and toric varieties

• Weeks 3-4, Chapter 2: Local properties, singularities, one-parameter subgroups

• Weeks 5-7, Chapter 3: Orbit-cone correspondence, divisors, line bundles and cohomology

• Weeks 8-10, Chapter 4 & 5: Moment map, tangent bundle, intersection theory, Serre duality, Betti numbers, Chow groups, Riemann-Roch and Bezout theorem

• Weeks 11-15, Beyond Fulton: Special topics (Log geometry? Spherical varieties?)

Resources

Here are some books/notes

• Introduction to Toric Varieties by Fulton

• Toric Varieties by Cox, Little Schneck

• Toric-Geometry, course notes by Dhruv Ranganathan

• Toric Notes, handwritten and scanned by Navid Nabijou Here are some problem sheets assigned by Navid in his toric geometry course:

• Example Sheet 1

• Example Sheet 2

• Example Sheet 3

• Example Sheet 4