Departement Mathematik und Statistik

Dolbeault Cohomology (HS 2015)

Lecturer

  • Dr. Rafael Andrist

Date and Venue

  • Monday, 10 - 12 h, B13 (ExWi)
  • Wednesday, 10 - 12 h, B13 (ExWi)
  • Start: Monday, September 14, 2015
  • End: October 30, 2015 (after the first half of the semester)

Details

  • 3 ECTS credit points
  • Enrollment for oral/written exam by the second last Friday of the lecture period via KSL
  • Further information (contents, exercise series, prerequisites etc.) on the course's ILIAS site
  • The course is intended for all Master students interested in geometry or in complex analysis. Knowledge of analysis in several complex variables is not required. However, basic knowledge about differentiable manifolds is assumed, and some familiarity with differential forms is helpful.
  • This course is intended for students in the following programs:
    • M.Sc. in Mathematics (Gefäss Analysis und Numerische Mathematik oder Gefäss Geometrie, Topologie)
    • M.Sc. in Statistics (Gefäss Mathematik)

Contents

  • Complex differential forms
  • The inhomogeneous Cauchy–Riemann equation
  • The Dolbeault lemma and Dolbeault cohomology
  • Hartogs' "Kugelsatz"
  • Čech cohomology and Dolbeault's theorem

Literature

  • Short lecture notes (in German) with proof sketches will be made available.
  • D. Huybrechts: Complex Geometry. Springer, 2005
  • J. L. Taylor: Several Complex Variables. AMS, 2002