MAGIC074: Algebraic Geometry

Course details

A core MAGIC course

Semester

Spring 2014
Monday, January 20th to Friday, March 28th

Hours

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

Timetable

Mondays
11:05 - 11:55
Fridays
13:05 - 13:55

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. The first 10 lectures will be delivered by Stephen Donkin; the second 10 by Ian McIntosh.

Prerequisites

Some familiarity with undergraduate commutative algebra (rings and their homomorphisms, ideals, quotient rings). It might be advisable to take MAGIC 073 (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; Complete and separated varieties; projective varieties are complete and separated; Chow's lemma (every complete irreducible variety is birational to a projective variety); algebraic curves and the Riemann-Roch theorem via sheaf theory.

Lecturers

  • SD

    Prof Steve Donkin

    University
    University of York
    Role
    Main contact
  • IM

    Dr Ian McIntosh

    University
    University of York

Bibliography

No bibliography has been specified for this course.

Assessment

Description

Assessment will be via a 3 hour take-home exam during the Spring assessment period (see the Calendar for this year's dates).

Assessment not available

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Files

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Lectures

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