Algebraic Geometry II

Teaching semester

Irregular

Objectives and Content

Objectives:

The course is an introduction to important topics in modern algebraic geometry, such as coherent sheaves, their cohomology, divisors and differentials.

Content:

Building up on the material covered in MAT320, this course brings the students deeper in the investigation of the geometry of schemes. The main topics are coherent sheaves, their cohomology, divisors and differentials, and the applications to the geometry of algebraic curves and surfaces.

Learning Outcomes

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

Knowledge

The student

• will know the definitions of the main object studied by algebraic geometry, will know the statements of the most important theorems and will be able to present a sketch of their proofs.

Skills

The student

• can use the fundamental tools that are important for many problems in modern algebraic geometry.
• is able to make short proofs of statements in algebraic geometry.
• has solid experience and training in reasoning with abstract mathematical structures.

General competence

The student

• is able to take a research article in algebraic geometry and read it 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.

Required Previous Knowledge

MAT320, MAT224

Recommended Previous Knowledge

MAT229 Algebraic Geometry I

Forms of Assessment

Oral examination

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.

Subject Overlap

M321: 15 ECTS