MAGIC074: Algebraic Geometry

Course details

A core MAGIC course

Semester

Spring 2025
Monday, January 27th to Friday, April 4th

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)

Course forum

Visit the https://maths-magic.ac.uk/forums/magic074-algebraic-geometry

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

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.

Assessment

The assessment for this course will be released on Tuesday 22nd April 2025 at 00:00 and is due in before Friday 2nd May 2025 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

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Lectures

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