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General


This course is part of the MAGIC core.

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.

Semester

Autumn 2019 (Monday, October 7 to Friday, December 13)

Hours

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

Timetable

  • Fri 09:05 - 09:55

Prerequisites

Familiarity with undergraduate commutative algebra (rings and their homomorphisms, ideals, quotient rings). It is 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;

Other courses that you may be interested in:

Lecturer


Valentina Di Proietto
Email V.Di-Proietto@exeter.ac.uk
Phone


Bibliography


Algebraic VarietiesKempf


Note:

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Assessment



The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. The total number of marks is 100. You will need a mark of 50 to pass.

No assignments have been set for this course.

Recorded Lectures


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