Algebraic Geometry (MAT630)

Introduction to algebraic geometry, emphasizing basic properties and examples of varieties and maps between varieties.


Course description for study year 2025-2026

See course description and exam/assesment information for this semester (2024-2025)
Facts

Course code

MAT630

Version

1

Credits (ECTS)

10

Semester tution start

Spring

Number of semesters

1

Exam semester

Spring

Language of instruction

English

Offered by
Time table

View course schedule

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

Individual oral exam

Course teacher(s)

Course coordinator:

Tyson Ritter

Course teacher:

David Ploog

Course teacher:

Martin Gunnar Gulbrandsen

Head of Department:

Bjørn Henrik Auestad

Method of work

4 hours lectures per week.

Open for

Admission to Single Courses at the Faculty of Science and Technology
Mathematics and Physics - Master of Science Degree Programme Mathematics and Physics - Five Year Integrated Master's Degree Programme

Admission requirements

Must meet the admission requirements of one of the study programmes the course is open for.

Course assessment

The faculty decides whether early dialogue should be conducted in all or selected groups of courses offered by the faculty. The purpose is to gather feedback from students for making changes and adjustments to the course during the current semester. In addition, a digital evaluation, students’ course evaluation, must be conducted at least once every three years. Its purpose is to collect students` experiences with the course

Literature

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