MATH5535 is a Special Topic in Pure Mathematics honours or master courses.   The Topic title is Introduction to Algebraic Geometry.  

Units of credit: 6

Prerequisites: MATH3701 and MATH3711.

Familiarity with modules and basics of category theory, introduced in MATH5735 is highly recommended. 

Cycle of offering: T2

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information:  The Course outline will be made available closer to the start of term - please visit this website: https://www.unsw.edu.au/course-outlines

Important additional information as of 2023

UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

If you are currently enrolled in MATH5535, you can log into UNSW Moodle for this course.

Course overview

The aim of this course is to put the theories of rings, fields and modules in a geometric context. This perspective is of fundamental importance in various branches of mathematics, including number theory, representation theory, differential geometry and mathematical physics.  In algebraic geometry varieties play the role of manifolds in differential geometry.

Our first aim is the study of affine and projective varieties and maps between them. Next, we will go through local properties of these objects and discuss what is meant by singularity. An important goal for this course is the study of the famous Riemann-Roch theorem for curves, for which we will need the notions of Divisors and Differential Forms.  Riemann-Roch traces a deep connection between topology and complex analysis, through purely algebraic methods. As such it provides a showcase for the power of algebro-geometric techniques. We will end the course by discussing a few applications of this theorem and briefly review some more advanced topics in the field.