Introduction to Algebraic Geometry

This is a course about the basics concepts of algebraic geometry dealing with affine and projective varieties, co-ordinate rings, morphisms, rational maps and elliptic curves.

Notes

(Updated on 25 April, 2013)

Comments and corrections are welcome.

Notes on algebra.

Examination

June 2012 exam, solutions and feedback.

Problem sheets

The solutions to all problem sheets are available in blackboard.

Handouts and related material

Affine transformations of conics
Affine equivalence of triangles
Examples of rational maps between affine varieties and animated images: circle, cuspidal cubic, nodal cubic, stereographic projection, figure 8 curve.
Examples of calculating singular points
Summary of the properties of projective varieties: handout or beamer (for online viewing)
Examples of rational maps and morphisms between projective varieties
Intersection multiplicities
Cubics through 8 points, black and white version for printing
Pascal's theorem
The group law on an elliptic curve
Examples of calculations on elliptic curves
Transforming the equation of an elliptic curve to Weierstraß form.

Coursework

The questions, feedback and solutions of the 2013 coursework assignment are now available.

The solutions of the coursework test.

The total coursework mark (out of 20) can be calculated by the formula 0.5*(test mark)+0.3*(coursework assignment mark).

Animations and videos

The course also has its own dedicated youtube channel.