## Algebraic Geometry (WS 2021/22)

Andreas Gathmann and Jonas Frank

### 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).