Aims

The aim of the module is to introduce and study  algebraic  curves in the real plane, the complex plane and the complex projective plane.  [Such curves are defined by a polynomial equation and the course involves an interplay between the geometry of the curves and the algebra of polynomials.]

Learning objectives

At the end of the module you should be familiar with and able to carry out operations related to curves in the complex affine plane and in the complex projective plane.

Syllabus

• the construction of the projective plane defined by a field;
•  the curve in the affine plane corresponding to a polynomial in two variables;
• the  curve in the projective plane corresponding to a homogeneous polynomial;
•  birational corresponence and rational curves;
• numerical properties of the intersection of two algebraic curves.

Recommended texts

• Elementary geometry of algebraic curves - an undergraduate introduction, C.G. Gibson,  Cambridge Univ. Press, 1998. (recommended)
• Algebraic Curves, R. J. Walker (out of print), more advanced
• Algebraic Curves, W. Fulton, advanced, free from www.math.lsa.umich.edu/~wfulton/CurveBook.pdf

Teaching

• Spring Term
• 3 lectures per week

Assessment

Example: Two hour closed examination in Summer Term (90%), Coursework (10%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

This module is not available as an elective

Prerequisites

• Advanced Algebra