ementas

Algebraic Geometry, HSE 2017.2

Programme

1. Schemes and their morphisms.
2. Fiber products and their applications.
3. Relative point of view.
4. Functor of points.
5. Separability, properness and projectivity.
6. Flatness and Hilbert polynomial.
7. Families of schemes and their limits.
8. Differentials, smoothness.
9. Coherent sheaves, their cohomology and higher direct images, semi-continuity theorem.
10. Proj, blow-up.
11. Geometric applications - curves, surfaces.

Prerequisites

Basics of

• commutative algebra,
• homological algebra,
• sheaf theory,
• an undergraduate course to algebraic geometry.

Keep in mind that this is a graduate course.

Homework: All exercises in Chapters II and III of Hartshorne.

Last read: 2017.2, HSE