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FSF3605 Algebraic Geometry II 7.5 credits

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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–)
Headings with content from the Course syllabus FSF3605 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Sheaves on topological spaces

  • Schemes, subschemes

  • Affine schemes, projective schemes

  • Fiber product

  • Proper morphisms

  • Quasi-coherent sheaves

  • Kähler differentials

  • Invertible sheaves, 0(1)

  • Defining properties of projective n-space

  • Weil divisors

  • Cartier divisors

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.

Literature

R. Hartshorne "Algebraic Geometry'', Chapter 2.

Supplementary reading in D. Mumford "The Red book of Vari­eties and Schemes".

Examination and completion

Grading scale

G

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.

If the course is discontinued, students may request to be examined during the following two academic years.

Homework assignments, and exercise sessions.

Other requirements for final grade

Approved assignments combined with problem-solvingsessions.

Examiner

Profile picture David Rydh

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.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

SCI/Mathematics

Education cycle

Third cycle

Postgraduate course

Postgraduate courses at SCI/Mathematics