Module MA341F: Algebraic Geometry
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Hilary term 201617
 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.
 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, blowups, 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 2hour 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.