Abstract: In the first part of the course we gave an introduction to the theory of toric varieties, i.e., varieties that are almost homogeneous under an algebraic torus action. In the second part, we turned to more general aspects of algebraic torus actions, such as Geometric Invariant Theory, Cox rings and polyhedral divisors.

Program: each morning 2 lectures, 90 min each, by Klaus Altmann (KA) and Juergen Hausen (JH) followed by 90 min excercise session in the afternoon and contributed talks in the evening. The following is a list of titles of lectures:

• JH: Algebraic torus actions, KA: Geometry of toric varieties
• JH: GIT of torus actions, KA: Deformation theory
• JH: Cox rings, KA: Deformations of toric varieties
• JH: Cox rings and combinatorics, Nathan Iilten: Polyhedral divisors

Readings:

• Altmann, Hausen, Polyhedral Divisors and Algebraic Torus Actions
• Arzhantsev, Derenthal, Hausen, Laface Cox rings
• Fulton, Introduction to toric varieties.
• Dolgachev, Lectures on invariant theory.
• Altmann, Deformation theory, DMV notes
• Cox, The Homogeneous Coordinate Ring of a Toric Variety
• Berchtold, Hausen, Cox rings and combinatorics

Organizer: Jaroslaw Wisniewski, Institute of Mathematics, Warsaw University.

Picture of participants

The school was financed by Institute of Mathematics of Warsaw University and by a grant from Polish Ministry of Science and Higher Education (grant N N201 2653 33).