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Algebraic Geometry (MAST90097)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

Availability
Semester 2 - On Campus
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This course is an introduction to algebraic geometry. Algebraic geometry is the study of zero sets of polynomials. It exploits the interplay between rings of functions and the underlying geometric objects on which they are defined. It is a fundamental tool in may areas of mathematics, including number theory, physics and differential geometry. The syllabus will cover affine and projective varieties, the Nullstellensatz, Zariski topology, morphisms, sheaves, schemes and may include additional topics in algebra and algebraic geometry (e.g., dimension, smoothness, singularities).

Intended learning outcomes

On completion of the subject, students should be able to:



  • explain and apply basic concepts and results from the theory of varieties and schemes;
  • calculate invariants of varieties;
  • apply sheaves to problems involving varieties and schemes;
  • solve problems about varieties and schemes by converting them into problems in algebra.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 19 November 2025