MAT9210 – Algebraic Geometry I
Schedule, syllabus and examination date
Changes in the course due to coronavirus Spring 2020
Teaching and examinations will take place digitally. This may result in changes to your schedule, mandatory activities, exam form and grading scale. See updated information on the semester page and in Canvas.
Introduction to algebraic curves and varieties.
Algebraic geometry is a classical subject with a modern face that studies geometric objects defined by polynomial equations in several variables.
The course introduces the basic objects in algebraic geometry: Affine and projective varieties and maps between them. It covers the concepts of dimension, singularities, curves and intersection theory form a geometric and an algebraic point of view. There is a particular emphasis on concrete examples.
After completing the course you:
- know the definitions and basic properties of algebraic varieties;
- know the relation between dimension in commutative rings and in algebraic sets;
- can perform computations with morphisms and rational maps between algebraic varieties;
- can decide whether an algebraic variety is singular;
- can use blowing up to resolve plane curve singularities;
- know the properties of the Hilbert polynomial and can compute it for selected projective varieties;
- know the Bezout theorem and can use it in geometric applications;
- know how to present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.
Admission to the course
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
- 10 credits overlap with MAT4210 – Algebraic Geometry I.
6 hours of lectures/exercises every week extending over half the spring term.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Final oral examination.
In addition, each PhD candidate is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more: