Algebraic Geometry

Subject 620-630 (2009)

Note: This is an archived Handbook entry from 2009. Search for this in the current handbook

Credit Points: 12.50
Level: 9 (Graduate/Postgraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2009:

Semester 2, - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable


Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 36 hours comprising 2 one-hour lectures per week and 1 one-hour computer lab/practical class per week.
Total Time Commitment: 3 contact hours plus 7 hours private study per week.
Prerequisites: None.
Corequisites: None.
Recommended Background Knowledge: It is recommended that students have completed a subject equivalent to 620636 Commutative Algebra.
Non Allowed Subjects: None.
Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit.


Dr Paul Timothy Norbury
Subject Overview: Algebraic geometry is the study of the zero sets of polynomials. As the name suggests, it combines algebra and geometry. It is a fundamental tool in many areas of mathematics, including differential geometry, number theory, integrable systems and in physics, such as string theory. Syllabus: Plane conics, cubics and the group law, genus of a curve, commutative algebra Noetherian rings, Zariski topology, the Nullstellensatz, coordinate ring of functions on a variety, projective varieties, singularities, divisors, Riemann Roch theorem.
Objectives: After completing this subject, students should gain:
- an appreciation of the geometry underlying commutative algebra, e.g. the geometry of the zero set of a polynomial;
- an understanding of the Nullstellensatz;
- a fundamental understanding of projective varieties;
- experience with the Zariski topology;
- applications of algebraic geometry to related areas such as differential geometry, number theory and physics.
- the ability to pursue further studies in this and related areas.
Assessment: Up to 60 pages of written assignments (60%: three assignments worth 20% each, due early, mid and late in semester), a 2 hour written examination (40%, in the examination period).
Prescribed Texts: TBA
Recommended Texts: TBA
Breadth Options:

This subject is not available as a breadth subject.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills: Upon completion of this subject, students should gain the following generic skills:
- Problem-solving skills including the ability to engage with unfamiliar problems and identify relevant solution strategies
- Analytical skills through the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis
- Through interactions with other students, the ability to work in a team
- Time management skills: the ability to meet regular deadlines while balancing competing commitments
Related Majors/Minors/Specialisations: R05 RM Master of Science - Mathematics and Statistics

Download PDF version.