Algebraic geometry II
- ECTS credits
- Teaching semesters
- Autumn, Spring
- Course code
- Number of semesters
- English if English-speaking students attend the lectures, otherwise Norwegian
Objectives and Content
The course is an introduction to sheaves and schemes in algebraic geometry and their fundamental properties. This forms the basis of modern algebraic geometry.
The course gives an introduction to the theory of sheaves and schemes. In particular, the notions affine, noetherian, integral, reduced, irreducible, separated, proper and projective schemes are considered, as well as closed and open embeddings, sheaves of modules, divisors, morphisms into projective spaces, differentials, smooth schemes and Bertini's theorem.
On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:
- is able to define and use fundamental notions and constructions and knows important results in algebraic geometry connected to sheaves and schemes, as well as morphisms between them
- is able to perform a simple analysis of schemes, in particular using properties of well-known sheaves.
- is able to produce the main ideas in the proofs of the most important results connected to the notions above.
- masters fundamental techniques within sheaf and scheme theory, and morphisms between schemes, in particular embeddings of schemes into projective spaces.
- is able to argue mathematically correct and present proofs and reasoning
- has solid experience and training in reasoning with sheaves and geometric stuctures
- is able to work individually and in groups
- is able to formulate in a precise and scientifically correct way
- is able to decide whether complex mathematical arguments are correct
Level of Study
Semester of Instruction
Irregular, course will be offered if it is on this course list: Workbook: Emneliste for innreisende utvekslingsstudenter (uhad.no)
Required Previous Knowledge
Recommended Previous Knowledge
Credit Reduction due to Course Overlap
MAT320: 5 ECTS
MAT321: 5 ECTS
MAT322: 5 ECTS