Algebraic Geometry

Textbook: We will primarily follow the following two lecture notes for our course:

Lecture 0: Review of rings and ideals, affine algebraic sets, Hilbert basis theorem
Lecture 1: Zariski topology, radical ideals, Hilbert Nullstellensatz
Lecture 2: Affine varieties, coordinate rings, irreducibility and prime ideals, Noetherian topological spaces
Lecture 3: Dimension of affine varieties, field of rational functions, regular functions
Lecture 4: Sheaf of regular functions, distinguished open sets, stalks
Lecture 5: Regular functions on distinguished opens, polynomial maps, morphisms of affine varieties
Lecture 6: Affine varieties and reduced finitely generated k-algebras, distinguished opens are affine
Lecture 7:
Lecture 8:
Lecture 9:
Lecture 10:
Lecture 11:
Lecture 12:
Lecture 13:
Lecture 14:
Lecture 15:
Lecture 16:
Lecture 17:
Lecture 18:

Spring 2026