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Symplectic toric geometry

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2022-2023
Duration: 
50 h
Description: 

After an introduction to toric geometry, where the main tool will be algebraic geometry, the course will explore the application of techniques from symplectic geometry, such as moment maps and symplectic quotients.

Syllabus:

  1. Fans and toric varieties 
  2. Orbit-cone correspondence 
  3. Singularities of toric varieties
  4. Completeness
  5. Divisors in toric varieties 
  6. Polytopes vs. divisors
  7. GIT construction of toric varieties 
  8. Elements of symplectic geometry 
  9. Moment maps
  10. Toric varieties as symplectic quotients. Delzant polytopes
  11. Toric metrics
Prerequisites: 
basic differential geometry, algebraic geometry (schemes, completeness, divisors, line bundles). More advanced tools in these topics will be introduced in the course.
Next Lectures: 

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