Andreas Gathmann - Algebraic Geometry (WS 2021/22)

Algebraic Geometry (WS 2021/22)

Dates and Times

Lecture: Tue 10:00-11:30 (48-538), Thu 10:00-11:30 (48-538), starting October 26
Example Class: Tue 16:00-17:30 (48-538), starting November 2
Holidays: December 20 - January 2

Class Notes

The lecture notes for this class are now finished, you can download them below. The modifications compared to the old notes of WS 2019/20 are not very large however, so you can clearly also use the old version e.g. for preparing for the exam.

If you use the current notes, and find any errors or have any suggestions for improvements, please tell me so that I can change the notes accordingly!

Complete notes (138 pages, last updated March 29, 2023)
Chapter 0: Introduction
Chapter 1: Affine Varieties
Chapter 2: The Zariski Topology
Chapter 3: The Sheaf of Regular Functions
Chapter 4: Morphisms
Chapter 5: Varieties
Chapter 6: Projective Varieties I: Topology
Chapter 7: Projective Varieties II: Ringed Spaces
Chapter 8: Grassmannians
Chapter 9: Birational Maps and Blowing Up
Chapter 10: Smooth Varieties
Chapter 11: The 27 Lines on a Smooth Cubic Surface
Chapter 12: Schemes
Chapter 13: Sheaves of Modules
Chapter 14: Quasi-coherent Sheaves
Chapter 15: Differentials
Chapter 16: Cohomology of Sheaves

Homework

Homework problems will be assigned every Thursday. They can be downloaded below and are due one week later (i.e. again on Thursday, at any time). Please submit your solutions online in the OLAT course.

Submitting homework solutions is not compulsory, but the content of the homework problems will be relevant for the final oral exam.

Problem set 1, due November 4
Problem set 2, due November 11
Problem set 3, due November 18
Problem set 4, due November 25
Problem set 5, due December 2
Problem set 6, due December 9
Problem set 7, due December 16
Problem set 8, due January 6
Problem set 9, due January 13
Problem set 10, due January 20
Problem set 11, due January 27
Problem set 12, due February 3

Questions?

If you have any questions – regarding the organisation, the lecture, the homework, or whatever – don't hesitate to contact us! You can talk to me after the lecture or ask Jonas in the example class, come to my office (48-517), write an e-mail (andreas@mathematik.uni-kl.de), or use the online forum in the OLAT course. Usually I can also easily be reached on our Mathematics Discord server (here you can find the invitation link).