MATH32062 Course Materials
Introduction to Algebraic GeometryThis 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.
ExaminationJune 2012 exam, solutions and feedback.
- Problem Sheet 1
- Problem Sheet 2
- Problem Sheet 3
- Problem Sheet 4
- Problem Sheet 5
- Problem Sheet 6
- Problem Sheet 7
- Problem Sheet 8
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.
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.
- Herwig Hauser's gallery of algebraic surfaces
- IMAGINARY, an exhibition of algebraic surfaces organised by Mathematisches Forschungsinstitut Oberwolfach.
- Advent calendar of algebraic surfaces
- Free software for drawing algebraic curves and surfaces
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