- Lecturer: Mateusz Michalek
- Date: Friday, 11:00 - 12:30
- Room: G3 10
- Language: English
- Target audience: MSc students, PhD students, Postdocs
- Keywords: Algebraic Varieties, Lattice Polytopes, Complex Torus, Lattice Cones, Divisors, Orbits, Singularities
- Prerequisites: Basic knowledge of algebraic geometry and commutative algebra (say at the level of nonlinear algebra Ringvorlesung) or a lot of motivation and enough time to catch up
Toric varieties form a special class of algebraic varieties, in some aspects generalizing aﬃne and projective spaces. Due to connections to combinatorics they also form one of the best understood classes. A lot of algebraic invariants turn out to behave in a particularly nice way for toric varieties. The aim of the lecture is to describe interactions of algebra, combinatorics and geometry; to learn about toric varieties, but at the same time gain experience in algebraic geometry.
We will be closely following the book ’Toric Varieties’ by Cox, Little and Schenck. The course will very actively involve participants - everyone will be expected to read the material in advance and some participants will be asked to present various parts. We hope to keep a fast pace, so that the course not only presents connections between polytopes/cones and toric varieties, but also describes more involved constructions including Cox rings, Picard and class groups, canonical divisor, sheaf co-homology, various types of singularities (including Gorenstein, Cohen-Macaulay, rational, normal) etc.