Details for Course FMA030F Algebraic Geometry

Current Established Course Syllabus

General

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.

Contents

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

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.

Judgement and Approach

Types of Instruction

Lectures
Comments:
If there are few participans, the course might be given as a self-study literature course

Examination Formats

Admission Requirements

Assumed Prior Knowledge

Selection Criteria

Literature

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

Further Information

Course code

Administrative Information

1 course syllabus.

Valid from	First hand in	Second hand in	Established
Spring 2014	2014‑04‑02 13:55:09	2014‑04‑02 13:58:55	2014‑05‑13

No matching course occasion was found.

1 course occasion.

Course syllabus valid from	Start Date	End Date	Published
Spring 2014	2016‑01‑21 (approximate)	2016‑03‑15