Commutative Algebra and Algebraic Geometry
10 credits
Syllabus, Master's level, 1MA276
A revised version of the syllabus is available.
- Code
- 1MA276
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 8 March 2018
- Responsible department
- Department of Mathematics
Entry requirements
120 credits including Algebraic Structures
Learning outcomes
In order to pass 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; sheaves and cohomology of sheaves; Picard groups; Enriques-Kodaira classification of surfaces.
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.