FSF3708 Computational Algebraic Geometry 7.5 credits

Computational methods in algebraic geometry, including for example implicitization and  blow-ups. 

The overall aim is to develop the computational skills within algebraic geometry among the participants.

At the end of the course the students should be able to: 

• Use implicitization to compute the defining equations of a variety given as the image of a map. 
• Compute the presentaion of the associated graded algebra of a local ring. 
• Compute blow-ups of projective varieties along smooth subvarieties
• Use standard pairs for integer programming problems
• Make computations in the Hilbert scheme of low degree Hilbert polynomials
• Compute stabilzers of monomial ideals
• Use eliminants and eigenvalue techniques to find the solutions to  polynomial systems of equations. 
• Write a package in Macaulay2 including documentation which makes it possible for others to use the code written in a project within a specialized area.

PhD students with sufficient knowledge in algebraic geometry and commutative algebra. 

Computations in algebraic geometry with Macaulay 2 by David Eisen bud, et al.

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

• INL1 - Assignment, 3.0 credits, grading scale: P, F
• PRO1 - Project work, 4.5 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 and project work with oral presentation.

Homework and project work with oral presentation

Mats Boij

• 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.