Mathematical Institute of the University of Bonn

Wintersemester 2020/21

Selected Topics in Algebraic Geometry: Toric Varieties (V5A4)

Lecturer: Dr. Alberto Cattaneo (cattaneo [at] math.uni-bonn.de)
Wednesday 14:15-16:00; ONLINE (Zoom).

Toric geometry is a highly interconnected discipline, which combines algebraic and convex geometry with combinatorics and discrete mathematics. It is also very concrete, providing a plethora of explicit examples to test general geometric tecnhiques and theories.
The course will present a broad introduction to toric varieties. An irreducible algebraic variety is called toric if it contains as a Zariski open subset an algebraic torus, whose action on itself extends to an algebraic action on the whole variety. We will see how to construct toric varieties from finite sets of characters and from fans of polyhedral cones, and we will investigate in detail the links between geometrical properties of the varieties and the combinatorial data used in their construction. We will then focus on the theory of sheaves on toric varieties (and their cohomology) and on singularity theory.

All details and materials are available on the ecampus page.

Prerequisites: commutative algebra and basic algebraic geometry (Hartshorne I-III).

Literature:

• D. A. Cox, J. B. Little, H. K. Schenck - Toric varieties (American Mathematical Society).
• W. Fulton - Introduction to toric varieties (Princeton University Press).