Course contents: a selection of the following topics

• properties of morphisms (proper, projective, smooth)
• divisors
• (quasi-)coherent sheaves
• cohomology
• Hilbert functions
• the Riemann-Roch Theorem

G.R. Kempf: Algebraic varieties. London Mathematical Society Lecture Note
Series. 172. Cambridge: Cambridge University Press. 1993. x, 163 p.

A. Schmitt: Homological algebra, lecture notes.

J.L. Taylor: Several complex variables with connections to algebraic
geometry and Lie groups. Graduate Studies in Mathematics. 46. Providence,
RI: American Mathematical Society. 2002. xvi, 507 p.