FMA030F

Tillfällig

Algebraic Geometry

6

Ren forskarutbildningskurs

7151 (Centre of Mathematical Sciences / Mathematics)

 -05-13

FN1/Anders Gustafsson

English

Vid tillräcklig efterfrågan

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.

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

* 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.

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.

Föreläsningar

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

Skriftlig tentamen

Muntlig tentamen

Underkänd, godkänd

Basic abstract algebra.

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

FMA030F

 -05-13

FN1/Anders Gustafsson