2020 – 2021, VI semester

Algebraic geometry is a part of mathematics studying algebraic varieties, i.e. curves, surfaces etc. that can be defined locally as a common zeroes of a polynomial family. Algebraic geometry is closely related to commutative algebra, which deals with commutative rings and modules over them.

The course is an introduction to commutative algebra and algebraic geometry. In commutative algebra we study properties of localizations and integral dependence, Hilbert’s Nullstellensatz and dimension theory of commutative rings. The geometric part of the course includes first properties of algebraic varieties, regular and rational maps, Weil and Cartier divisors, and local properties. We also pay attention to so-called arithmetic case, i.e. varieties over fields that are not algebraically closed.

Up to 50% of time will be left for a seminar classes. As a result of mastering the course, students will be able to use algebraic geometry in the study of related subjects, in scientific research and practical applications.