Course: Algebraic Geometry
Programme:
- Schemes and their morphisms.
- Fiber products and their applications.
- Relative point of view.
- Functor of points.
- Separability, properness and projectivity
- Flatness and Hilbert polynomial
- Families of schemes and their limits
- Differentials, smoothness.
- Coherent sheaves, their cohomology and higher direct images, semi-continuity theorem.
- Proj, blow-up.
- 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:
2020.2, online,
2017.2, HSE.