*Course Syllabus for*
# 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.

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

**Examination formats:** Written exam, oral exam

**Grading scale:** Failed, pass

**Examiner:**

## Admission Details

**Assumed prior knowledge:** Basic abstract algebra.

## Course Occasion Information

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