MAGIC074: Algebraic Geometry

Course details

A core MAGIC course

Semester

Autumn 2025
Monday, October 6th to Friday, December 12th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Timetable

Mondays
14:05 - 14:55 (UK)
Mondays
15:05 - 15:55 (UK)

Description

A first course in algebraic geometry, giving you a solid basis for the study of problems that use algebro-geometric language.

Prerequisites

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. 

Syllabus

  • Affine, projective and quasiprojective varieties.
  • Rational, birational and regular maps.
  • Dimension. Singular and non-singular points. Tangent space.
  • Divisors and differential forms. Riemann-Roch Theorem for curves.
  • Blow-ups and intersection theory for smooth complex surfaces (time permitting).

Lecturer

  • Jesus Martinez Garcia

    Jesus Martinez Garcia

    University
    University of Essex

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Monday 12th January 2026 at 00:00 and is due in before Friday 23rd January 2026 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.

Files

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

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.