Algebraic Surfaces

2026/2027

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered by:

Faculty of Mathematics

Type:

Optional course (faculty)

When:

3, 4 module

Instructor

Avilov, Artem

Course Syllabus

Abstract

Algebraic geometry originated as a study of solution sets for systems of algebraic equations, but it soon became clear that these objects (known as algebraic varieties) are interesting in their own right. The main invariant of such a variety is its dimension: the higher the dimension, the more complex and intricate the structure becomes. Studying high-dimensional algebraic geometry requires a solid understanding of lower-dimensional varieties. Last year we studied the simplest non-trivial case — algebraic curves of dimension one. This semester will focus on the next level of complexity: algebraic surfaces (dimension two). These are much richer and diverse compared to curves, necessitating new methods and techniques. We'll explore various types of surfaces and examine fundamental properties within each class.