Module MA341F: Algebraic Geometry
- Credit weighting (ECTS)
- Semester/term taught
Hilary term 2016-17
- Contact Hours
11 weeks, 3 lectures including tutorials per week
- 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.
- Module Content
- Curves and surfaces.
- Affine varieties.
- Projective varieties.
- Functions on varieties, the Zariski topology, and the Nullstellensatz
- Bezout's theorem
- 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. The supplemental examination paper, if required, will determine 100% of the supplemental module mark.