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MAU34302 Introduction to algebraic geometry

Module Code MAU34302
Module Title Introduction to algebraic geometry
Semester taught Semester 2
ECTS Credits 5
Module Lecturer Prof. Andreea Nicoara
Module Prerequisites
 
MAU22102 Fields, rings and modules and
MAU23206 Calculus on manifolds

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 2.
  • Continuous assessment contributes 20% towards the overall mark.
  • Re-assessment, if needed, consists of 100% exam.

Contact Hours

11 weeks of teaching with 3 lectures per week.

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.
  • Provide definitions, prove theorems and provide either examples or counterexamples for various concepts related to algebraic geometry.

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.