Algebraic Geometry
Algebraisk geometri

FMA030F, 6 credits

Valid from: Spring 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-05-13

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

Aim

The aim of the course is to prepare postgraduate students for research using Gröbner bases for solving and interpreting systems of polynomial equations in several variables mainly within algebraic geometry.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must * vara väl bekant med begreppet Gröbnerbas och förstå varför de be well acquainted with the concept of a Gröbner basis and understand why they are useful for solving systems of polynomial equations.

Competences and Skills

For a passing grade the doctoral student must

• be able to reproduce key results and give rigorous and detailed proofs of them,
• be able to compare key results,
• be able to apply the basic techniques, results and concepts of the course to concrete examples and exercises,
• be able to combine concepts from the course with other important topics in algebra.

Course Contents

Affine varieties and ideals in the ring of polynomials. Gröbner bases. Elimination theory. Algebraic-Geometric Correspondences. Polynomial and Rational Functions on a Variety.

Course Literature

Cox, David A. & Little, John B.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, 2007. ISBN 9780387356518.

Instruction Details

Type of instruction: Lectures. If there are few participans, the course might be given as a self-study literature course

Examination Details

Examination formats: Written exam, oral exam
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: Basic abstract algebra.

Course Occasion Information

Contact and Other Information

Course coordinator: Victor Ufnarovski <victor.ufnarovski@math.lth.se>