Final Projects.

For a final project you should choose a topic about toric varieties and either give a 25 minute talk in class or write up a report about it.

Below is a list of topics to choose from, but you can also find a different topic that interests you. This list will be updated with new topics as the semester progresses.

If you are giving a talk, try not to cram too much material into it. In 25 minutes you have barely enough time to explain the definitions and some examples. Your goal should be to explain a notion in toric geometry to other students, not really prove theorems.

The topics below are very general. Each topic has enough material for several talks.

  1.  Normal polytopes. A good reference here is the Oberwolfach workshop report. It describes the main problem and many approaches to it. Each of these approaches could be one talk. Here are a couple of topics for talks:
  2. Reflexive polytopes. Reflexive polytopes are lattice polytopes whose polar dual is also a lattice polytope. They are interesting in both combinatorics and algebraic geometry.
  3. Toric vector bundles.
  4. The homogeneous coordinate ring of toric varieties.
  5. Toric varieties as quotients.