(1) Convex polyhedra and toric varieties: Convex polyhedral cones. Affine toric varieties. Fans and toric varieties. Toric varieties from polyhedra.

 (2) Singularities and compactness: Local properties of toric varieties. Surfaces, quotient singularities. One-parameter subgroups, limit points. Compactness and properness. Nonsingular surfaces. Resolution of singularities.

(3) Orbits, topology, and line bundles: Orbits. Fundamental groups and Euler characteristics. Divisors. Line bundles. Cohomology of line bundles.

(4) Moment map and the tangent bundle: Manifolds with singular corners. Moment map. Differentials and the tangent bundle. Serre duality. Betti numbers.

(5) Intersection theory: Chow groups. Cohomology of nonsingular toric varieties. Riemann-Roch theorem. Mixed volumes. Bézout theorem.

Prerequisites: Algebra B-3, Algebraic Geometry I

Bibliography:

Cox D. A., Little J. B., and Schenck H. K.  Toric Varieties. AMS, 2011

Ewald G.  Combinatorial convexity and algebraic geometry. Springer, 1996

Fulton W.  Introduction to toric varieties. Princeton, 1993