# Toric Geometry and Sage

**Abstract:** I will give a pedagogical introduction to toric geometry without requiring previous knowledge in algebraic geometry. The lecture series will be based on the toric geometry package in the open-source Sage (http://www.sagemath.org) mathematics software system. Various examples relevant to string theory are used to illustrate the techniques. Each lecture will contain exercises to be solved in the accompanying computer lab.

**Preliminary lecture plan:**

Tuesday, April 26: Videos

- Affine algebraic varieties and affine toric varieties
- Python, Cython, and Sage in scientific computing
- Resolution of singularities

Wednesday, April 27: Videos

- Local to global: Coordinate patches and compact varieties
- Fans and lattice polytopes
- What is the Chow group

Thursday, April 28: Videos

- Homogeneous coordinates for toric varieties
- Divisors and line bundles
- Kahler and Mori cones

Friday, April 29: Videos

- Calabi-Yau hypersurfaces and complete intersections
- Periods and Picard-Fuchs equations
- Mirror symmetry

**References:** David A. Cox, John B. Little, Hal Schenck: "Toric Varieties" (http://www.cs.amherst.edu/~dac/toric.html). Free download until the print version is published!