# Module MA341F: Algebraic Geometry

**Credit weighting (ECTS)**- 5 credits
**Semester/term taught**- Hilary term 2018-19
**Contact Hours**- 11 weeks, 3 lectures including tutorials per week
**Lecturer**- Prof Andreea Nicoara
**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.
- Define concepts, prove theorems, and write down examples and counterexamples.

- 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.
**Module Prerequisite**- Fields, Rings, and Modules (MA2314) and Calculus on Manifolds (MA2322)
**Assessment Detail**- This module will be examined in a 2-hour
**examination**in Trinity term. The final mark is 80% of the exam mark plus 20% continuous assessment consisting of a certain number of homework sets assigned throughout the term.

**Module Content**