On successful completion of this module, students will be able to:

Work with curves, surfaces, projective and affine varieties.

Understand the relationship between commutative algebra and geometry that underlies this field as well as its connections to number theory and complex analysis.

Define concepts, prove theorems, and write down examples and counterexamples.

Module Content

Curves and surfaces.

Affine varieties.

Projective varieties.

Functions on varieties, the Zariski topology, and the Nullstellensatz

Bezout's theorem

Tangent spaces and dimension

Singularities, blow-ups, and the resolution of singularities.

Module Prerequisite

Fields, Rings, and Modules (MA2314) and Calculus on Manifolds (MA2322)

Assessment Detail

This module will be examined in a 2-hour examination in Trinity term. The final mark is 80% of the exam mark plus 20% continuous assessment consisting of a certain number of homework sets assigned throughout the term. The supplemental examination paper, if required, will determine 100% of the supplemental module mark.