## Algebraic Geometry (WS 2019/20)

Andreas Gathmann and Kevin Kühn

### Dates and Times

*Lecture:*Tue 10:00-11:30 (48-519), Thu 10:00-11:30 (48-519), starting October 29*Example Class:*Tue 1:45-3:15 (36-265), starting November 5*Holidays:*November 1, December 23 - January 4

### Class Notes

The notes for this class are now finished, you can download them below.

Starting with chapter 12 I have written these notes more or less from scratch, so there will probably still be (hopefully minor) errors and inconsistencies. If you find any of them please let me know so that I can correct them! Also, compared to the lecture I changed and added a few small things to make everything more consistent. Of course, anything changed or added after the end of the class will not be relevant for the oral exams.

- Complete notes (138 pages, last updated March 13, 2020)
- 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 put your solutions in Kevin's mailbox next to 48-210. You can submit them in groups of up to 3 students.

- Problem set 1, due November 7
- Problem set 2, due November 14
- Problem set 3, due November 21
- Problem set 4, due November 28
- Problem set 5, due December 5
- Problem set 6, due December 12
- Problem set 7, due December 19
- Problem set 8, due January 9
- Problem set 9, due January 16
- Problem set 10, due January 23
- Problem set 11, due January 30
- Problem set 12, due February 6