Semester tution start
Language of instruction
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.
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
MAT250 Abstract Algebra, MAT510 Manifolds
Form of assessment
Method of work
4 hours lectures per week.
Mathematics and Physics - Master of Science Degree Programme
Mathematics and Physics - Five Year Integrated Master's Degree Programme
There must be an early dialogue between the course coordinator, the student representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.
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