algebraic geometry III

Postgraduate course

Course description

Objectives and Content


The course is an introduction to the cohomology of sheaves, as well as algebraic curves and surfaces within algebraic geometry.


The course gives an introduction to the theory of cohomology of sheaves applied to schemes, like for instance Cech cohomology and Serre duality, as well as basic theory of algebraic curves, such as the Riemann-Roch theorem, the Riemann-Hurwitz theorem, Clifford¿s theorem, embeddings into projective spaces, and of algebraic surfaces, like intersection theory, the Riemann-Roch theorem and blowing ups.

Learning Outcomes

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:


The student

  • is able to define and use fundamental notions and constructions and knows important results in algebraic geometry connected to the cohomology of sheaves, algebraic curves and surfaces, as well as morphisms between them
  • is able to analyse schemes and morphisms using cohomology of sheaves
  • is able to produce the main ideas in the proofs of the most important results connected to the notions above.


The student

  • is able to use the fundamental techniques that are important in many problems in algebraic geometry
  • is able to produce short proofs of statements in algebraic geometry
  • has solid experience and training in reasoning with abstract mathematical stuctures

General competence

The student

  • is able to read a research article in algebraic geometry independently (with some effort).
  • is able to follow the introduction of a research talk in algebraic geometry.
  • is able to follow a colloquium talk in algebraic geometry.

ECTS Credits


Level of Study


Semester of Instruction

Irregular, course will be offered if it is on this course list: Workbook: Emneliste for innreisende utvekslingsstudenter (
Required Previous Knowledge
Credit Reduction due to Course Overlap
MAT322: 10 ECTS
Access to the Course
Access to the course requires admission to a master¿s or PhD programme at The Faculty of Mathematics and Natural Sciences
Compulsory Assignments and Attendance
Forms of Assessment
Oral Exam
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Assessment Semester
Each semester
Reading List
The reading list will be available within June 1st for the autumn semester and December 1st for the spring semester
Course Evaluation
The course will be evaluated by the students in accordance with the quality assurance system at UiB and the department
Examination Support Material
Programme Committee
The Programme Committee is responsible for the content, structure and quality of the study programme and courses.
Course Administrator
Department of Mathematics