Course

Algebraic Geometry (MAT630)

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


Dette er emnebeskrivelsen for studieåret 2025-2026

Fakta

Emnekode

MAT630

Vekting (stp)

10

Semester undervisningsstart

Spring

Undervisningsspråk

English

Antall semestre

1

Vurderingssemester

Spring

Timeplan

Vis timeplan

Litteratur

Søk etter pensumlitteratur i Leganto

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.

Forkunnskapskrav

Ingen

Anbefalte forkunnskaper

Abstract Algebra (MAT250), Manifolds (MAT510)

Exam

Form of assessment Weight Duration Marks Aid
Oral exam 1/1 45 Minutes Letter grades None permitted


Individual oral exam

Fagperson(er)

Head of Department:

Bjørn Henrik Auestad

Course teacher:

Martin Gunnar Gulbrandsen

Course coordinator:

Tyson Ritter

Course teacher:

David Ploog

Method of work

4 hours lectures per week.

Åpent for

Mathematics and Physics - Master of Science Degree Programme Mathematics and Physics - Five Year Integrated Master's Degree Programme

Emneevaluering

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 course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

Kontakt

Head of Department:

Bjørn Henrik Auestad

Course teacher:

Martin Gunnar Gulbrandsen

Course coordinator:

Tyson Ritter

Course teacher:

David Ploog

Tilbys av

Faculty of Science and Technology

Department of Mathematics and Physics

The course description is retrieved from FS (Felles studentsystem). Version 1