Course

Algebraic Geometry (MAT630)

Facts

Course code MAT630

Credits (ECTS) 10

Semester tution start Spring

Language of instruction English

Number of semesters 1

Exam semester Spring

Time table View course schedule

Literature The syllabus can be found in Leganto

Introduction

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

Content

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

Abstract Algebra (MAT250), Manifolds (MAT510)

Exam

Oral exam

Weight 1/1

Duration 45 Minutes

Marks Letter grades

Aid None permitted

Individual oral exam

Method of work

4 hours lectures per week.

Open for

Admission to Single Courses at Master Level at the Faculty of Science and Technology
Mathematics and Physics - Master Mathematics and Physics - Master

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 will be held in all courses or in selected groups of courses. The aim is to collect student feedback for improvements during the semester. In addition, a digital course evaluation must be conducted at least every three years to gather students’ experiences.

Contact

Head of Department:
Bjørn Henrik Auestad
Course teacher:
Martin Gunnar Gulbrandsen
Course coordinator:
Tyson Ritter
Course teacher:
David Ploog

Offered by

Faculty of Science and Technology

Department of Mathematics and Physics

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