Entry requirements

120 credits including Modules and Homological Algebra. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• report on fundamental concepts in commutative algebra and how they relate to algebraic geometry;
• explain and exemplify the main objects in algebraic geometry such as affine and projective varieties
• reproduce central theorems regarding curves and surfaces
• use methods from the course to solve problems in algebraic geometry

Content

Commutative algebra: rings, modules, localization, chain conditions, completions and dimension theory. Algebraic geometry: affine and projective varieties; functions, morphisms and rational maps; resolution of singularities for curves; Riemann-Roch and Riemann-Hurwitz for curves; basic theory of schemes and sheaves; cohomology of sheaves; Picard groups.

Instruction

Lectures and problem solving sessions

Assessment

Written examination at the end of the course and assignments given during the course, according to instructions given at the beginning of the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.