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Module MA341F: Algebraic Geometry

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2016-17
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, 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.