Faculty of Science

Algebraic Geometry (AlgGeo)
Provider: Faculty of Science

Activity no.: 5580-22-07-31
	Enrollment deadline: 25/04/2022

Place

Department of Mathematical Sciences

Date and time

25.04.2022, at: 08:00 - 24.06.2022, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Søren G E-mail address: galatius@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 4

Scheme group

Exam form

Oral examination

Exam form

30 minutes preparation, 30 minutes oral examination including grade determination

Exam details

Exam registration requirements: To be eligible to take the exam the student must have handed in the mandatory homework assignment, and this must have been approved. Aid: Only certain aids allowed. All aids allowed for the preparation. For the oral exam, the student may bring 1 A4 sheet of notes.

Grading scale

7 point grading scale. For PhD students: Passed / Not Passed

Course workload

Course workload category	Hours
Lectures	35.00
Exam	1.00
Exercises	21.00
Preparation	149.00

Sum	206.00

Content

Algebraic Geometry is the study of geometric structures arising from solution sets of polynomial equations, and forms a central part of modern mathematics. It has numerous applications, ranging from number theory to theoretical physics.

The course will be an introduction to Algebraic Geometry, and will cover the following topics:
- Algebraic sets, affine and projective varieties, fundamental properties of varieties.
- Sheaves and locally ringed spaces.
- Morphisms of varieties, birational maps and blow-ups.
- Smoothness and singularities.
- Hilbert polynomials and Bezout's theorem.

Learning outcome

Knowledge: To display knowledge and understanding of the course topics and content at a level suitable for further studies in Algebraic Geometry.

Skills: At the end of the course the student is expected to be able to follow and reproduce arguments at a high abstract level corresponding to the contents of the course.

Competences: At the end of the course the student is expected to be able to apply basic techniques and results to concrete examples.

Teaching and learning methods

5 hours lectures and 3 hours exercises each week for 7 weeks

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