Complex Manifolds 2025

• Prerequisites: analytic functions and basics about de Rham cohomology
• Lecture outline
• Summary of GAGA, see also the notes of P. Achinger
• Problem sheets:
  • 10 October
  • 17 October
  • 24 October
  • 31 October → 7 November
  • 21 November → 28 November
  • 5 December
  • 12 December
  • 19 December
  • 9 January 2026 → 16 January
  • 23 January 2026, solution to 3.1
    
    Written exam: 29 January 14-16, room 3130
  • Examples of problems for written exam
  • Solutions to the written exam
    
  • List of questions for oral exam, 3 questions will be randomly chosen from the list.

  Bibliography

  • D. Huybrechts: Complex geometry. An introduction (Universitext) - the main texbook for this course
  • P. Griffiths, J. Harris: Principles of algebraic geometry (initial chapters)
  • Donu Arapura: Algebraic Geometry over the Complex Numbers (Universitext)
  • C. Voisin: Hodge Theory and Complex Algebraic (Cambridge Studies in Advanced Mathematics)
  • Mark A. de Cataldo: Lectures on the Hodge theory of projective manifolds (Summary of the Hodge theory, there is also a book edition)
  
  

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  Grading rules: exercises 30%, oral exam preceded by a written test 35% + 35%
• Questions for the oral exam 2022
  

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