Toric Geometry
Toric geometry is the study of toric varieties, a class of algebraic varieties that are defined using combinatorics. There is a correspondence between algebro-geometric properties of toric varieties and combinatorial data. This makes toric geometry ideal for computations and provides a rich source of examples of algebraic varieties. Toric geometry has become a fundamental tool in modern algebraic geometry.
Lecturer
Date
13th August, 2026 ~ -
Prerequisite
Undergraduate courses in geometry and algebra (especially topology, polynomial rings, ideals), some knowledge of algebraic geometry (Zariski-closed sets in affine or projective space over an algebraically closed field).
Syllabus
1. Affine and projective toric varieties.
2. Toric varieties constructed from polyhedral fans.
3. Divisors on toric varieties.
4. Toric varieties and geometric invariant theory quotients.
2. Toric varieties constructed from polyhedral fans.
3. Divisors on toric varieties.
4. Toric varieties and geometric invariant theory quotients.
Reference
David A. Cox, John B. Little, and Henry K. Schenck, Toric varieties, Graduate Studies in Mathematics, vol. 124, American Mathematical Society, Providence, RI, 2011.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
No
Notes Public
No
Language
English