Department
of Mathematics
Math 510- Fall 2006
Algebraic Curves and Riemann Surfaces
TTh at 9:00-10:20am in 241 Altgeld Hall
Instructor | Text | Grading | Resources | Homework | News and Announcements
This course is part ``introduction to complex differential geometry'' and part ``introduction to algebraic geometry''. The intersection of these two subjects is nowhere better exemplified than in the theory of compact Riemann Surfaces, or equivalently, complex algebraic curves. For this reason, as well as for their intrinsic beauty, we focus on the objects listed in the Course Title. We will closely follow the book `Introduction to Algebraic Curves' by Phillip Griffiths. Our goal is to work through the entire book.
Professor Steven Bradlow [bradlow@uiuc.edu]
Office: 259Altgeld
Office Hours: TBA, or by appointment
News and Information
8/29/06: There will be no class on Tuesday September 4 or Thursday September 6.
Make-up lectures will be scheduled on Tuesdays at 4pm – dates and locations to be announced.
9/18/06: Make-up lectures
There will be make-up lectures this Tuesday (September 19) and next (September 26) at 5pm in Altgeld 145.
We have the room booked for 90 minutes. The actual length of the class will depend on the energy level of students and/or lecturer.
9/21/06: Homework 2 is available here
10/15/06: Homework 3 is available here
11/17/06: Homework 4 is available here
Introduction to Algebraic Curves by Phillip A. Griffiths, Translations of Mathematical Monographs, Vol. 76, published by the AMS
There will be a take-home exam. This may be split up into one or more problem sets assigned during the course of the semester. Write-ups should be done on your own, but you may freely discuss the assignments with your classmates or with any other appropriate experts.
There are many good books on Riemann Surfaces and Algebraic Curves. The following is by no means an exhaustive list, but contains a selection of books that are either particularly accessible, or close in spirit to the theme of this course, or both!
· Riemann Surfaces by H. Farkas and
· Compact Riemann Surfaces by Jurgen Jost , Springer
· Complex Algebraic Curves by
Francis Kirwan, LMS Student Texts Vol 23,
· Algebraic Curves and Riemann Surfaces by Rick Miranda, AMS Graduate Studies in Mathematics, Volume 5 (1995)
· Algebraic Curves by William Fulton, Mathematics Lecture Notes Series, Bejamin/Cummings (1969)
Wikipedia entry for Algebraic Curves and for Riemann Surfaces
Homework
· Homework 1 (dvi / pdf ) [Due date: Tuesday September 11] Note: in the version handed out in class on 8/29/06 Question 2 is not correctly stated.
· Homework 2 (dvi / pdf ) [Due date: Tuesday October 3]
· Homework 3 (dvi / pdf ) [Due date: Tuesday October 29]
· Homework 4 (dvi / pdf ) [Due date: Tuesday December 5]
Last modified November 17, 2006