Algebraic Geometry (MAT630)
Introduction to algebraic geometry, emphasizing basic properties and examples of varieties and maps between varieties.
Course description for study year 2024-2025. Please note that changes may occur.
Facts
Course code
MAT630
Version
1
Credits (ECTS)
10
Semester tution start
Spring
Number of semesters
1
Exam semester
Spring
Language of instruction
English
Time table
Content
NB! This is an elective course and may be cancelled if fewer than 10 students are enrolled by January 20th for the spring semester.
Affine and projective varieties, the Zariski topology, regular and rational maps. A selection of examples, such as Grassmannians, blowups, lines on cubic surfaces, or the Bézout Theorem.
Learning outcome
After completing this course, the student is able to:
- Reproduce and exemplify the definitions of affine and projective varieties, the Zariski topology, and regular and rational maps.
- Analyse the geometry of manageable examples of varieties, such as determining the dimension, the irreducible components, and other central properties.
- Explain relations between geometric questions for varieties and algebraic questions for commutative rings.
- Carry out and convey reasoning about varieties and about regular and rational maps.
Required prerequisite knowledge
None
Recommended prerequisites
MAT250 Abstract Algebra, MAT510 Manifolds
Exam
| Form of assessment | Weight | Duration | Marks | Aid |
|---|---|---|---|---|
| Oral exam | 1/1 | 45 Minutes | Letter grades | None permitted |
Course teacher(s)
Course coordinator:
Tyson RitterCourse teacher:
David PloogCourse teacher:
Martin Gunnar GulbrandsenHead of Department:
Bjørn Henrik AuestadMethod of work
4 hours lectures per week.
Open for
Course assessment
There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.