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MAT630_1

Algebraic Geometry

This is the study programme for 2019/2020. It is subject to change.


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

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.

Contents

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.

Required prerequisite knowledge

None.

Recommended previous knowledge

MAT250 Abstract Algebra
You may advantageously take MAT600 Topology and symmetry at the same time.

Exam

Weight Duration Marks Aid
Oral exam1/145 minutesA - FNone permitted

Course teacher(s)

Course coordinator
Martin Gunnar Gulbrandsen
Course teacher
Martin Gunnar Gulbrandsen
Head of Department
Bjørn Henrik Auestad

Method of work

4 hours lectures.

Open to

Master studies at the Faculty of Science and Technology.

Course assessment

Usually by forms and/or discussion according to university regulations.

Literature

Gathmann: Algebraic Geometry.


This is the study programme for 2019/2020. It is subject to change.

Sist oppdatert: 13.11.2019

History