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

Course forum

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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

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Assessment

Description

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.

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Lectures

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