Week February 18-20:
Presentation of the course.
Algebraic varieties and morphisms.
Sheaves.
Locally free sheaves and vector bundles.
Week February 25-27:
No lectures
Week March 3:
Invertible sheaves and line bundles.
Order of vanishing of a rational function along divisor.
Weil divisors and Cartier divisors.
The Picard group of a variety.
Week March 10-12: (online)
Linear systems.
Morphisms to the projective space.
Complete linear systems.
Base locus of a linear system.
Base point freeness, ampleness and very ampleness.
Quick introduction to sheaf cohomology.
Cech cohomology.
Examples.