2025/2026

Toric Varieties

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Karine Kuyumzhiyan

Language: English

Contact hours: 72

Course Syllabus

Abstract

"Given a convex polytope, there is a way to construct an algebraic variety starting from this polytope. The obtained varieties are called \textit{toric}. For example, from a simplex of dimension~$n$ we obtain the projective space $\mathbb P^n$. The most important algebro\Д geometric properties of toric varieties can be expressed in terms of combinatorial properties of their polytopes, so many algebraic and geometric invariants of toric varieties can be easily computed. So toric varieties serve as test varieties for different algebro\Д geometric hypotheses, become examples and counterexamples etc."