Introduction to Algebraic Geometry

1. i Affine algebraic sets; Hilbert’s Nullstellensatz; function fields; Krull dimension.
2. ii Graded rings; (quasi-)projective varieties; rational functions.
3. iii Algebraic plane curves; morphisms; products; finite maps.
4. iv Normality; Noether normalisation; birational morphisms.
5. v Tangent spaces; non-singularity; resolution of singularities; blowing up points.
6. vi Divisors; Bézout’s theorem on curves; class groups.
7. vii Intersection numbers; the Riemann–Roch theorem.

Course syllabus (PDF)

1. 01 Assignment 1 PDF ↗