Level 5 - Complex Algebraic Curves

Complex Algebraic Curves
Level 5

Winter 2008

Course description

This one term course provides an introduction to complex algebraic curves. The goal is to give a flavour of both the algebro-geometric and the complex-analytic points of view. Here is a brief course description.

The class meets in room 417 of the Mathematics Building from 2pm-3pm on Mondays, Tuesdays.

The examples class will take place in room 214a on Wednesdays 1pm-2pm.

Lecture notes and Homework assignments

The lecture notes and homework assignments that are made available may be downloaded from here:

Week 1: Affine space, radical ideals and affine varieties (Assignment 1);
Week 2: Coordinate rings and morphisms of affine varieties (Assignment 2);
Week 3: Noether normalisation and the Nullstellensatz (Assignment 3);
Week 4: Projective space, homogeneous ideals and projective varieties (Assignment 4);
Week 5: Rational functions and morphisms of projective varieties (Assignment 5);
Week 6: Hilbert polynomial, Bezout's theorem and the degree-genus formula (Assignment 6);
Week 7: Singularities and dimension (Reading assignment on Riemann surfaces)
Week 8: The Weierstrass function and elliptic curves (Assignment 8);
Week 9: The normal form for cubic curves and the group law (Assignment 9);
Week 10: Riemann-Roch and the Kodaira Embedding theorem for curves (Essay assignments).

References

The primary references for the course are:

Complex Algebraic Curves by F. Kirwan, LMS Student texts 23.
Algebraic curves by W. Fulton (don't buy at amazon's laughable price!)

Other books that you may find useful include:

Undergraduate algebraic geometry by M. Reid. LMS Student texts 12.
Introduction to Algebraic Curves by P. Griffiths, AMS Translations 76.
Undergraduate commutative algebra by M. Reid. LMS Student texts 29.

Mathematics Department,
University of Glasgow, University Gardens,
Glasgow G12 8QW, Scotland.

Office: Mathematics Building, room 427
Phone: 632-4005
Email: craw at maths dot gla dot ac dot uk

Complex Algebraic Curves Level 5

Complex Algebraic Curves
Level 5