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Algebraic Geometry

Key information

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Module description


Dvir’s proof of Kakeya conjecture over finite fields. Bezout’s theorem for curves. Affine and projective algebraic varieties, the Hilbert basis theorem, the Hilbert Nullstellensatz, rational/algebraic maps between algebraic varieties. Dimension, tangent space, and non-singularity for an algebraic variety.


Linear Algebra, rings and modules, topology. 

Assessment details

2 hr written examination or alternative assessment

Educational aims & objectives

The aim of this module is to introduce the basic notions of algebraic geometry including algebraic varieties and algebraic maps between them. Along the way, you will encounter many examples and will see how theorems in algebra can be used to prove geometric results about algebraic varieties.

Teaching pattern

Two hours of lectures and one hour of tutorial per week throughout the term

Suggested reading list

Indicative reading list - link to Leganto system where you can search with module code for lists

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.