Arnold Sommerfeld Center

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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 ( 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" ( Free download until the print version is published!