MAU34302 Introduction to algebraic geometry
| Module Code | MAU34302 |
|---|---|
| Module Title | Introduction to algebraic geometry |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Andreea Nicoara |
| Module Prerequisites |
MAU22102 Fields, rings and modules and
MAU23206 Calculus on manifolds |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Work with curves, surfaces, projective and affine varieties.
- Understand the relationship between commutative algebra and geometry that underlies this field as well as its connections to number theory and complex analysis.
- Provide definitions, prove theorems and provide either examples or counterexamples for various concepts related to algebraic geometry.
Module Content
- Curves and surfaces, affine varieties, projective varieties.
- Functions on varieties, the Zariski topology, and the Nullstellensatz.
- Tangent spaces and dimension.
- Singularities, blow-ups, and the resolution of singularities.