MAGIC074: Algebraic Geometry

Course details

A core MAGIC course


Spring 2024
Monday, January 29th to Friday, March 22nd; Monday, April 22nd to Friday, May 3rd


Live lecture hours
Recorded lecture hours
Total advised study hours


14:05 - 14:55 (UK)

Course forum

Visit the MAGIC074 forum


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.


  • Jesus Martinez Garcia

    Jesus Martinez Garcia

    University of Essex


Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.


The assessment for this course will be released on Monday 13th May 2024 at 00:00 and is due in before Friday 24th May 2024 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.


Only current consortium members and subscribers have access to these files.

Please log in to view course materials.


Please log in to view lecture recordings.