Algebraic Geometry II, Wintersemester 2021/22

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

Assistentin: Dr. Zhixin Xie
Sprechstunde: Nach Vereinbarung per Email.

NEWS (October 2021)

The course begins on Tuesday, 19 October 2021. The lectures will take place online and the exercise classes will take place in presence.

The course will be taught in English.

The recorded Video-Lectures (see below) will be uploaded weekly. Each video will be available online for two weeks and then deleted.

To register for the Exercise Classes: please send an email to Dr. Tsakanikas tsakanikas [add @math.uni-sb.de]. This email should include also the following data: Name, Surname, Matrikelnummer and the your Uni Saar email address.

Dates: Tuesdays and Thursdays 10-12

Topics

The content includes: 

  • morphisms between sheaves and schemes
  • abstract varieties
  • properness and separatedness
  • sheaves of modules, invertible sheaves and divisors
  • projective morphisms, basepoint free divisors, ample divisors, blowups
  • 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, Algebraic Geometry I.

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 solution should then be sent to the Tutor by email or via Microsoft Teams. 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. Xie (your Prüfungssekretariat has to send us a confirmation that you are allowed to take part in the exam in time before the exam). If your Prüfungsordnung allows it, you may use the second try to improve the grade.

Video-Lectures

Exercise Session

  1. Thursdays 14-16 (Tutor: Dr. Zhixin Xie)

Literature

Campus-Bibliothek für Informatik und Mathematik prepared the literature list for this course here.

Exercise Sheets

Exercise sheets will be distributed via Microsoft Teams and the solutions should be returned to the Tutor via Microsoft Teams or via Email.

Address

Fachrichtung Mathematik
Campus, Gebäude E2 4
Universität des Saarlandes
66123 Saarbrücken
Germany