| 1 | Course Introduction, Zariski Topology | |
| 2 | Affine Varieties | Problem Set 1 due |
| 3 | Projective Varieties, Noether Normalization | |
| 4 | Grassmannians, Finite and Affine Morphisms | Problem Set 2 due |
| 5 | More on Finite Morphisms and Irreducible Varieties | |
| 6 | Function Field, Dominant Maps | Problem Set 3 due |
| 7 | Product of Varieties, Separatedness | |
| 8 | Product Topology, Complete Varieties | Problem Set 4 due |
| 9 | Chow's Lemma, Blowups | |
| 10 | Sheaves, Invertible Sheaves on P1
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| 11 | Sheaf Functors and Quasi-coherent Sheaves | Problem Set 5 due |
| 12 | Quasi-coherent and Coherent Sheaves | |
| 13 | Invertible Sheaves | Problem Set 6 due |
| 14 | (Quasi)coherent Sheaves on Projective Spaces | |
| 15 | Divisors and the Picard Group | |
| 16 | Bezout's Theorem | Problem Set 7 due |
| 17 | Abel-Jacobi Map, Elliptic Curves | |
| 18 | Kähler Differentials | Problem Set 8 due |
| 19 | Smoothness, Canonical Bundles, the Adjunction Formula | |
| 20 | (Co)tangent Bundles of Grassmannians | Problem Set 9 due |
| 21 | Riemann-Hurwitz Formula, Chevalley's Theorem | |
| 22 | Bertini's Theorem, Coherent Sheves on Curves | |
| 23 | Derived Functors, Existence of Sheaf Cohomology | Problem Set 10 due |
| 24 | Birkhoff–Grothendieck, Riemann-Roch, Serre Duality | |
| 25 | Proof of Serre Duality | Problem Set 11 due |
