Algebraic Geometry, Wintersemester 2026/27

Dozent: Prof. Dr. Vladimir Lazić
Sprechstunde: Nach Vereinbarung per Email.

Assistent: Dr. Massimiliano Alessandro
Sprechstunde: Nach Vereinbarung per Email.

The course will be held in English.

Registration for the exercise sessions: here.

If a lecture takes place online, then the recorded Video-Lecture will be uploaded to the CMS website of the course. Each video will be available online for two weeks and then deleted.

Dates: Tuesdays 16-18 in SR10, Wednesdays 10-12 in SR10

Topics

The content includes:

sheaves and schemes
morphisms between sheaves and schemes
abstract varieties
properness and separatedness
projective morphisms, basepoint free divisors, ample divisors, blowups
sheaves of modules, invertible sheaves and divisors
differentials and canonical sheaves, smoothness revisited
cohomology of sheaves, Čech cohomology
Serre duality, Riemann-Roch on curves
morphisms with connested fibres, Iitaka fibrations.

Prerequisites: Linear Algebra I and II, Algebra, Commutative Algebra and Introduction to Algebraic Geometry (recommended).

Exam Criteria

Example Sheets will appear on this webpage each week, which have to be solved until the following week (exception: see the first Example Sheet). The solutions should be uploaded to the CMS. The Sheets will be corrected and returned in the exercise sessions.

In order to obtain a grade, the following criteria are to be fulfilled: at least 50% of the points from the exercise sheets attained, and the passed exam.

Exam Dates

The exam will be an oral exam, the dates will be individually arranged.

Important: If you cannot register in the LSF for the exam, please send an email to Dr. Alessandro (your Prüfungssekretariat has to send us a confirmation that you are allowed to take part in the exam well in time before the exam). If your Prüfungsordnung allows it, you may use the second try to improve the grade.