Algebraic Geometry I

Wintersemester 2025/2026

Algebraic geometry is a branch of mathematics that combines algebra and geometry. Its main subject is the study of algebraic varieties, which can be understood as the solution sets of polynomial equations. The goal of this course is to introduce the language and fundamental concepts of algebraic geometry. Topics to be covered include affine and projective varieties and their morphisms, rational maps, smoothness, tangent spaces, and an introduction to the theory of sheaves and schemes.

Time and place:

Monday and Wednesday at 12-14 in Room A027.

Exercises: Thursday at 12-14 in B039, begins 23.10.
Extra Tutorium will take place on Wednesday 21.01. in B 052.

The written exam will take place on Thursday 05.02., 12:00-14:00, in Room B 047.
No aids are permitted in the examination. Please bring your student ID and a photo ID with you.
Exam
Solutions
The Klausureinsicht will take place on Friday 13.02. at 12:00 - 13:00 in my office B426 (if possible: Family Name A-N at 12:00-12:30, Family Name O-Z at 12:30-13:00).
Please double-check your grades; the wrong file was uploaded earlier.
Exam results

Literature:

R. Hartshorne, Algebraic geometry.
Qing Liu, Algebraic geometry and arithmetic curves.

Exercise sheets:

Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Sheet 7
Sheet 8 solution (Exercise 1)
Sheet 9
Sheet 10
Sheet 11
Sheet 12 solution (Exercise 3,4)