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Algebraic Geometry (AlgGeo)
Provider: Faculty of Science

Activity no.: 5580-22-07-31 
Enrollment deadline: 25/04/2022
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time25.04.2022, at: 08:00 - 24.06.2022, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserSøren G    E-mail address: galatius@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupC
Exam formOral examination
Exam form30 minutes preparation, 30 minutes oral examination including grade determination
Exam detailsExam 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 scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures35.00
Exam1.00
Exercises21.00
Preparation149.00
Sum206.00
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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