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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

Spring 2016 (Monday, January 11 to Friday, March 18)

Timetable

  • Wed 10:05 - 10:55

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;

Lecturer


Michael Bate
Email michael.bate@york.ac.uk
Phone 01904323026


Students


Photo of Abeer Al Balahi
Abeer Al Balahi
(East Anglia)
Photo of Mehsin Al-Showali
Mehsin Al-Showali
(Leicester)
Photo of Gareth Case
Gareth Case
(Lancaster)
Photo of Lorenzo De Biase
Lorenzo De Biase
(Cardiff)
Photo of Adam DENT
Adam DENT
(Leeds)
Photo of Aeran Fleming
Aeran Fleming
(Liverpool)
Photo of Xin Fu
Xin Fu
(Southampton)
Photo of Daniel Graves
Daniel Graves
(Sheffield)
Photo of Nicol Leong
Nicol Leong
(York)
Photo of Abigail Linton
Abigail Linton
(Southampton)
Photo of Robert Little
Robert Little
(Durham)
Photo of Stephen Nand Lal
Stephen Nand Lal
(Liverpool)
Photo of Angelo Rendina
Angelo Rendina
(Sheffield)
Photo of Will Rushworth
Will Rushworth
(Durham)
Photo of Harriet Serocold
Harriet Serocold
(Lancaster)
Photo of Amit Shah
Amit Shah
(Leeds)
Photo of Roberto Sisca
Roberto Sisca
(Surrey)
Photo of Fabio Strazzeri
Fabio Strazzeri
(Southampton)
Photo of ANON STUDENT
ANON STUDENT
(*External)
Photo of Isobel Webster
Isobel Webster
(Leeds)
Photo of Ariel Weiss
Ariel Weiss
(Sheffield)


Bibliography


Algebraic VarietiesKempf


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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 via a single take-home paper in April with 2 weeks to complete and submit online. There will be a choice of 2 out of 3 questions, and a pass will be awarded if your script is judged to be correct on at least half of the material chosen.

MAGIC074 Algebraic Geometry Exam

Files:Exam paper
Released: Monday 18 April 2016 (523.7 days ago)
Deadline: Friday 29 April 2016 (511.7 days ago)
Instructions:

Follow the instructions on the exam.



Recorded Lectures


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