Title:  Toric varieties

   Among the most accessible classes of algebraic varieties
are toric varieties.   This is fortunate for these are also among
the most commonly encountered outside of algebraic geometry 
within mathematics and in the applications of algebraic 
geometry.  Toric varieties in particular are currently
widely studied in algebraic geometry and its applications.

   This course would introduce the students to toric varieties,
emphasizing their fundamental combinatorial nature while focusing
on concrete examples and explaining some of their applications.

  Because of the elementary nature of these varieties, the
prerequisite will be graduate algebra, although courses in
commutative algebra and algebraic geometry will be helpful.

Here is an Outline:
 -Toric ideals
    Generation of toric ideals
    Groebner bases
    Computation
 -Affine toric varieties
 -Projective toric varieties
    Orbit decomposition and Limiting behavior
 -Lattice Polytopes
    Algebraic-Combinatorial Geometric Dictionary
    Normality of Sturmfellian Toric Varieties
 -Real projective toric varieties
    Irrational toric varieties
    Algebraic moment map
 -Geometric combinatorics, lattices and fans
 -Abstract Construction of Toric Varieties
    Arithmetic toric varieties
 -Cox/Delzant quotient construction
    Cox Coordinate Ring
  Line bundles on toric varieties
  Toric Degenerations

Grading will be based on class participation and a project/presentation at the end of the course

There are two texts that may accompany the class,
 - Toric Varieties by Wm Fulton (this book is hard to get)
 - Toric Varieties by Cox, Little, and Schenck
 - Ibadan Lectures on Toric Varieties (Notes that I have from a summer school)