Andreas Gathmann - Plane Algebraic Curves (SS 2023)

Plane Algebraic Curves (SS 2023)

News

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Dates and Times

Lecture: Mon 13:45-15:15 (48-538), starting April 17
Example class: Fri 11:45-13:15 (48-438), biweekly starting May 5
Holidays: May 1 (Tag der Arbeit), May 29 (Pfingstmontag)
Substitute dates: Wed May 3 and May 31, 10:00-11:30 (48-538)

Homework assignments

Homework problems will be assigned biweekly on Mondays, starting on April 24. They can be downloaded below and are due on Tuesdays one week later (at any time). You can put your solutions in Cedric's mailbox next to 48-210 or upload them as a PDF file in the Submissions tab of the OLAT course. You can submit them in groups of up to 3 students. Of course, in this case everyone should have their fair share both in finding and writing down the solutions; it is expected that everyone can explain their solutions on the blackboard in the example sessions. If you submit your solutions online as a group, only one of you should upload them and indicate the names of all participants on the solution.

Problem set 1, due May 2
Problem set 2, due May 16
Problem set 3, due May 30
Problem set 4, due June 13
Problem set 5, due June 27
Problem set 6, due July 11

Class Notes

The updated lecture notes for this class are now finished, you can download them below. If you use these notes, and find any errors or have any suggestions for improvements, please tell me so that I can change the notes accordingly!

Video recordings of the class are available on the page of the class notes.

Complete notes (71 pages, last updated October 21, 2023)
Chapter 0: Introduction
Chapter 1: Affine Curves
Chapter 2: Intersection Multiplicities
Chapter 3: Projective Curves
Chapter 4: Bézout's Theorem
Chapter 5: Applications of Bézout's Theorem
Chapter 6: Functions and Divisors
Chapter 7: Elliptic Curves
Chapter 8: The Riemann-Roch Theorem

Credits

You will get a certificate for this class if you attend the example classes regularly and score at least 1 out of 4 points in at least 70% of the homework problems.

Literature

There is no need to use any further literature besides the notes above. However, it can sometimes be helpful for the understanding of the material to read about it somewhere else in other words. If you want to have a look at some books for this reason, here is a small selection for the beginning:

W. Fulton: Algebraic Curves (2008)
E. Kunz: Introduction to Plane Algebraic Curves, Birkhäuser (2005)
F. Kirwan: Complex Algebraic Curves, Cambridge University Press (1995)

Questions?

If you have any questions – about the organization of the course, the lecture, the homework problems or whatever – do not hesitate to contact us! You can write an e-mail or in the forum, ask Cedric (cbrendel@rptu.de), talk to me after the lecture or just come at any time to my office (andreas@mathematik.uni-kl.de, 48-517).