FSF3612 Complex Algebraic Geometry 7.5 credits

The course ist fiven as a series of lectures (approx 15x2h). 

• complex manifolds, meromorphic functions, holomorphic vector bundles
• projective space, blow-ups, complex tori
• cohomology of complex manifolds
• some central theorems (such as Serre duality, Lefschetz (1,1)-theorem, Kodaira's embedding theorem)

After completing the course, the student should be able to

• prove properties of fundamental concepts in complex algebraic geometry; and
• draw conclusions about compact complex manifolds using techniques and theorems.

Master degree in mathematics, or equivalent.

Suitable prerequisites are

• a course in complex analysis,
• a course in differential geometry, and
• a course in algebra (e.g., algebraic topology or commutative algebra).

Main text-book: D. Huybrechts, Complex geometry: an introduction, Springer, 2005.

If the course is discontinued, students may request to be examined during the following two academic years.

• ÖVN1 - Exercises, 7.5 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The course is examined through homework exercises.

Assignments completed.

David Rydh

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.