MAGIC074: Algebraic Geometry

Course details

A core MAGIC course


Spring 2023
Monday, January 23rd to Friday, March 31st


Live lecture hours
Recorded lecture hours
Total advised study hours


12:05 - 12:55 (UK)


A first course in algebraic geometry, as the study of ringed spaces (of functions), which is a half-way house between classical algebraic geometry and modern scheme theory.


Familiarity with undergraduate commutative algebra (rings and their homomorphisms, ideals, quotient rings). It is advisable to take MAGIC073 (Commutative Algebra) in parallel. No prior knowledge of algebraic geometry is assumed. 


  • Varieties (affine, projective and ringed spaces) and their morphisms
  • Affine varieties as MaxSpec(A)
  • Geometry via the Nullstellensatz
  • The Zariski topology
  • The Hilbert basis theorem and the Noetherian property
  • Irreducibility, dimension and tangent spaces
  • Affine and finite morphisms
  • Hypersurfaces
  • Projective spaces and the Segre embedding.


  • Eleonore Faber

    Eleonore Faber

    University of Leeds


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The assessment for this course will be released on Monday 1st May 2023 at 00:00 and is due in before Monday 15th May 2023 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


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