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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.
  

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.

 

 

 

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.