Math 8140: Introduction to Combinatorial Algebraic Geometry

This is a topics course on algebraic varieties with combiantorial structure, focusing on toric varieties, rational projective homogeneous spaces ("G/P"), and related objects.  We will emphasize explicit descriptions of these spaces and their geometry.

Classes are on Monday, Wednesday, and Friday, 1:50 - 2:45pm, in MW 154.

There is no single textbook for the course. I will send notes and references by email, and eventually post some here.

For toric varieties, there are many excellent sources. Here are some I know and like:

• Fulton, Introduction to Toric Varieties
• Mustata, Lectures on Toric Varieties
• Cox, Little, and Schenck, Toric Varieties
• Oda, Convex Bodies and Algebraic Geometry
• Miller and Sturmfels, Combinatorial Commutative Algebra (Chapter 10)

Here are some notes on Lie theory background:

• LieTheory1
• LieTheory2
• LieTheory3