Lecture course
Algebraic Surfaces

Winter semester 2022/23
  • Time:  Monday, 8:30 - 10:30
  • Place:  25.22-03.73
  • Start: Monday, October 10
  • Lecturer: Prof. Dr. Stefan Schroeer
  • Teaching assistant: Dr. Cesar Hilario 

The course is tought in English, and aimed at master students who seek  to specialize in the area of algebraic geometry in particular those who plan to write a master thesis under my guidance. It may also be interesting for doctoral students and members of the GRK 2240 who want to gain a thorough understanding of this research area.


Content:  In this sepcialized lecture course we study the so-called Enriques classification of algebraic surfaces. Particular topics: intersection numbers and numerical group, Hodge Index Theorem, minimal models, formulas of Riemann--Roch and Noether, Chern numbers, rational surfaces, surfaces with trivial canonical class.

Literature:
L. Badescu: Algebraic surfaces
A. Beauville: Complex algebraic surfaces
D. Mumford: Letures on curves on an algebraic surface
V. Iskovskikh, I. Shfarevich: Algebraic surfaces
W. Barth, K. Hulek, C.  Peters, A. Van de Ven: Compact complex surfaces

Exercise sheets:    Sheet 1, Sheet 2, Sheet 3, Sheet 4, Sheet 5, Sheet 6


Learning platform ILIAS

We encourage you to discuss and solve the exercise sheets in working groups. Hand-ins, however, must be individual and handwritten.
Wie bearbeitet man ein Übungsblatt? (Von Prof. Manfred Lehn)
Exercise class:  

Class 1
 Tuesday, 14:30 - 16:00  in 25.22-00.81
 Dr. Cesar Hilario

Start: Second week of lecture period. Registration for lecture course and excercise class via HISLSF.
Examinations: oral, conducted in German or English.

Office hours:  
Prof. Dr. Stefan Schröer: Tuesday, 10:30 - 11:30
Dr. Cesar Hilario: Wednesday, 13:30-14:30