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.
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.
Three hours of lectures each week, together with a one-hour tutorial.
Suggested reading list
Suggested reading/resources (link to My Reading Lists)