Course - Algebraic Geometry - MA8203
MA8203 - Algebraic Geometry
Lessons are not given in the academic year 2019/2020
The course introduces the central concepts of algebraic geometry. Affine and projective varieties are introduced, and these and their morphisms are studied.
The concept of a sheaf on a topological space is introduced, and in particular affine and projective varieties are interpreted as the locally ringed spaces. Sheaves of modules and the concept of sheafification are discussed.
Beyond these basic concepts the content of the course may vary, and include for instance divisors, resolutions of singularities, Riemann-Roch theorem for curves, elliptic curves, Bezouts theorem, sheaf cohomology, schemes.
The course is taught every third year, next time Spring 2021. If there are few students, there will be guided self-study.
The student knows the basic concepts of algebraic geometry, in particular algebraic varieties with their structure sheaves, and the categories of coherent sheaves on these.
Further the student is familiar with some more advanced subjects, depending on the course content that year.
The students should learn the topics mentioned above and be able to apply these concepts in own research.
Learning methods and activities
Lectures, some tasks for homework, alternatively as guided self-study.
Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.
Recommended previous knowledge
MA8202 Commutative algebra.
Required previous knowledge
Participants need some knowledge of (commutative) rings and modules, in particular the definitions of these. Moreover they should know the concept of localization of a commutative ring with respect to a multiplicative subset.
Will be announced at the start of the course.
- * The location (room) for a written examination is published 3 days before examination date.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"