General information

Course type AMUPIE
Module title Algebraic curves
Language Enghlish
Module lecturer prof. dr hab. Wojciech Gajda
Lecturer's email
Lecturer position professor
Faculty Faculty of Mathematics and Computer Science
Semester 2024/2025 (summer)
Duration 60
USOS code 000


Module aim (aims)

This is an introductory course in algebraic geometry aimed at students of mathematics of all specializations. We will start with setting up firm foundations and discuss in detail theory of curves over complexes and then more generally over any algebraically closed field. Next we turn to affine and projective algebraic varieties and explain morphisms, local rings, function fields, dimension and nonsingular varieties. This will allow us to prove Riemann-Roch over an algebraically closed field. The main aim of the course is to introduce students to the basics of algebraic geometry, explore a large variety of different examples, and prove some important theorems of the trade.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

Knowledge of abstract algebra at the level of an undergraduate level: Groups, Rings an Fields will be very helpful.



Week 1  

Conics and Cubics 

Week 2 

Higher degree curves 

Week 3 

Bezout Theorem 

Week 4 

Riemann-Roch Theorem 

Week 5 

Riemann-Roch II 

Week 6 

Affine varieties I 

Week 7 

Affine varieties II 

Week 8  

Affine varieties III 

Week 9 


Week 10 


Week 11 

Projective varieties I 

Week 12 

Projective varieties II 

Reading list