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# Details for Course FMA030F Algebraic Geometry

General
• FMA030F
• Temporary
Course Name
• Algebraic Geometry
Course Extent
• 6
Type of Instruction
• Third-cycle course
• 7151 (Centre of Mathematical Sciences / Mathematics)
•  -05-13
• FN1/Anders Gustafsson

## Current Established Course Syllabus

General
• English
• If sufficient demand
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
• For a passing grade the doctoral student must
Types 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
• Failed, pass
Assumed Prior Knowledge
• Basic abstract algebra.
Selection Criteria
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
• FMA030F
•  -05-13
• FN1/Anders Gustafsson

## All Established Course Syllabi

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

## Current or Upcoming Published Course Occasion

No matching course occasion was found.

## All Published Course Occasions

1 course occasion.

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