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Sheaves on topological spaces
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Schemes, subschemes
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Affine schemes, projective schemes
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Fiber product
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Proper morphisms
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Quasi-coherent sheaves
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Kähler differentials
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Invertible sheaves, 0(1)
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Defining properties of projective n-space
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Weil divisors
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Cartier divisors
FSF3605 Algebraic Geometry II 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3605 (Spring 2019–)Content and learning outcomes
Course contents
Intended learning outcomes
After the course the student will have sufficient depth in the field to be able to pursue research in algebraic geometry.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in Mathematics.
Some knowledge in abstract algebra, as for instance SF2737 Commutative Algebra and Algebraic Geometry or equivalent.
Recommended prerequisites
Equipment
Literature
R. Hartshorne "Algebraic Geometry'', Chapter 2.
Supplementary reading in D. Mumford "The Red book of Varieties and Schemes".
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- HEM1 - Home assignments, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Homework assignments, and exercise sessions.
Other requirements for final grade
Approved assignments combined with problem-solvingsessions.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.