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Algebraic Geometry

 

Key information

  • Module code:

    7CCMMS20T

  • Level:

    7

  • Semester:

      Spring

  • Credit value:

    15

Module description

Syllabus

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.

Prerequisites

Linear Algebra, rings and modules, topology.

Assessment details

Assessment

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

Three hours of lectures each week, together with a one-hour tutorial.

Suggested reading list

Suggested reading/resources (link to My Reading Lists)