Announcements


There are no announcements

Forum

General


Description

The purpose of the course is to present enough material on compact Riemann surfaces for students to be able to read literature where ideas such as meromorphic differentials, Abel's map and the Jacobi variety, divisor classes and divisor line bundles are used. Compact Riemann surfaces are also the simplest examples of Kaehler manifolds, and every complete smooth algebraic curve is a compact Riemann surface, so they provide an entry into complex manifold theory as well as algebraic geometry. While sheaf theory provides an elegant way of treating many of the topics covered, it will not be explicitly invoked but we will take an approach (and use notation) which is in the spirit of analytic sheaf theory.

Semester

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

Timetable

  • Tue 10:05 - 10:55

Prerequisites

The approach we take will rely on a good grounding in complex analysis and a little point set topology. Some experience of the differential geometry of surfaces will be helpful.

Syllabus

Riemann surface as a complex manifold (motivated by multi-valued functions); vector fields and differential forms; basics of integration and singular homology for curves on surfaces; the Abel-Jacobi map and Abel's theorem; the Riemann-Roch theorem; (maybe get as far as Weierstrass points).

Lecturer


Ian McIntosh
Email ian.mcintosh@york.ac.uk
Phone (01904) 323094
Interests Differential geometry
Photo of Ian McIntosh


Students


Photo of Zhe Chen
Zhe Chen
(Durham)
Photo of Lorenzo De Biase
Lorenzo De Biase
(Cardiff)
Photo of Daniel Evans
Daniel Evans
(Liverpool)
Photo of Calum Horrobin
Calum Horrobin
(Loughborough)
Photo of John Lawson
John Lawson
(Durham)
Photo of Sarah Liddell
Sarah Liddell
(Leeds)
Photo of Robert Little
Robert Little
(Durham)
Photo of Joe Oliver
Joe Oliver
(Leeds)
Photo of Sam Povall
Sam Povall
(Liverpool)
Photo of Nimit Rana
Nimit Rana
(York)
Photo of Max Strachan
Max Strachan
(York)
Photo of ANON STUDENT
ANON STUDENT
(*External)
Photo of Ariel Weiss
Ariel Weiss
(Sheffield)


Bibliography


Complex algebraic curvesKirwan
Algebraic curves and Riemann surfacesMiranda
Lectures on Riemann surfacesForster


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



Assessment will be by a single take home examination during the Spring assessment period. The exam will have three questions, of which you will be asked to attempt two. To obtain a pass will require the equivalent of one complete correct answer to one question.

MAGIC006 exam 2016

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

There are 3 questions on the paper. Submit solutions to at most two questions. A pass will be awarded for the equivalent of one complete correct solution to one question.



Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-101exCRS.pdf
1-101solCRS.pdf
1-102exCRS.pdf
1-102solCRS.pdf
1-103exCRS.pdf
1-103solCRS.pdf
1-10CRSnotes_full.pdf
1-2L1-2_CRS.pdfL
3-5L3-4_CRS.pdfL
5-7L5-6_CRS.pdfL
7-9L7-8_CRS.pdfL
8-10L9-10_CRS.pdfL


Recorded Lectures


Please log in to view lecture recordings.