Syllabus
1. the spectrum of a commutative ring and its relation to algebraic varieties,
2. geometric aspects of localization of rings,
3. maps between varieties,
4. abstract varieties,
5. projective varieties and their properties,
6. Krull dimension.
Annotation
The course serves as an introduction to basic aspects of algebraic geometry. The discussed material includes the Zariski spectrum of a commutative ring and its relation to algebraic varieties, geometric aspects of localization of rings, maps between varieties, certain properties of abstract and projective varieties, and local properties of varieties (especially the Krull dimension and its properties).