MAGIC074: Algebraic Geometry

Course details

A core MAGIC course

Semester

Spring 2021
Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Mondays
12:05 - 12:55 (UK)

Description

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.

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

  • 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.

Lecturer

  • Eleonore Faber

    Eleonore Faber

    University
    University of Leeds

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 Monday 10th May 2021 at 00:00 and is due in before Monday 24th May 2021 at 11:00.

The exam for MAGIC074 Algebraic Geometry will be a take-home paper to be set on May 10 with deadline for submission being May 23, 23:59 (UK time). In order to pass the exam at least 50% need to be obtained.

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

Files

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Lectures

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