2318
From Mathsoc wiki
2318: Elementary projective and algebraic geometry
Lecturer: Dr. Calin Lazariou
Website: Link
Contents |
Introduction
The course
Inside the lecture theater you will probably find (one of) the most interesting pure mathematics courses taught at Trinity. The lectures are intense, as is the lecturer. Most of the course is dedicated to building up a good aul' knowledge of commutative algebra with a (quite a bit more than) smattering of order theory and set theoretic notions, culminating in Hilbert's Nullstellensatz and the classical Algebraic Geometry of the Italian school [1]. A fairly deep introduction to algebraic number theory(by undergraduate standards) also makes its way into things.
Actually this course covers a lot of things you should know but are not taught. Logic, posets, rigour &c. You should probably give it a go.
The subject
Algebraic geometry is the study of curves and surfaces described by polynomials in higher dimensions using the tools of commutative algebra. The classical theory was brought to its most advanced form by the Italian school in the early 19th century, but later extended by the French mathematicians notably Grothendieck's and his method of schemes along with Serre. Its applications are wide and often very powerful. A good example is Fermat's last theorem in Number Theory proved by Wiles in 1994, but whose proof was made possible only by the vast theory described by Serre and Grothendieck in the 60's and 70's.
Resources
The notes are more than sufficient for the first question in the exam, but for extra reading try the following. Note that the primer on algebraic curves related to the final three questions on the paper.
- Lang's Algebra
- Roman's Lattices and ordered sets
- Plane Curve Singularities
