Toric varieties are varieties with a torus action such that one orbit of the action is dense. They are excellent examples of many phenomena in algebraic geometry and an excellent first test for many conjectures, though in other ways they are completely unrepresentative as they are all rational with rational singularities. Toric varieties are naturally associated to polytopal fans (unions of cones) and projective toric varieties are naturally associated to polytopes in such a way that many of their properties can be combinatorially calculated from properties of the fans or polytopes.

Our aim is to read through Fulton's orange book on the subject. This is most likely too ambitious a goal, but I think three chapters will be realistic. We will meet Fridays at 3:30, starting with an organizational meeting on April 4. We agreed to change the meeting time to Mondays at 3:15. This change is effective April 14; we will still meet on April 11. Our meeting today (Friday Apr. 11) is at 3:30 due to a scheduling conflict.

The emphasis and approach of Fulton's book is geometric. Knowledge of schemes is not necessary, though he does use the construction of gluing varieties along open sets. (If you understand this in the context of manifolds, that should be sufficient background.) In a few of the later sections, some acquaintance with sheaves and cohomology might be useful, but we will proceed at an appropriate pace.

• _Introduction to Toric Varieties_, by William Fulton. This is an orange book, put out by Princeton University Press in its Annals of Mathematics Studies series.