| # |
Date |
Topic (references) |
Sections |
| 1 | 8 Sep | Plane curves | 1.1-1.3 |
| 2 | 10 Sep | Tangent lines | 1.4 |
|
| 3 | 13 Sep | Transcendence degree and dual curve | 1.5-1.6 |
| 4 | 15 Sep | Resultants | 1.7 |
| 5 | 17 Sep | Nodes and cusps and Hensel's lemma | 1.8-1.9 |
|
| 6 | 20 Sep | Bezout's theorem and Plücker formulas | 1.10-1.11 |
| 7 | 22 Sep | Zariski topology | 2.1-2.3 |
| 8 | 24 Sep | Nullstellensatz | 2.4-2.5 |
|
| 9 | 27 Sep | Morphisms of affine varieties | 2.6 |
| 10 | 29 Sep | Finite group actions | 2.7 |
| 11 | 1 Oct | Projective varieties, product varieties | 3.1-3.3 |
|
| 12 | 4 Oct | Morphisms of projective varieties | 3.4 |
| 13 | 6 Oct | Affine communication lemma | 3.5-3.6 |
| 14 | 8 Oct | The Nakyama Lemma | 4.1 |
|
| 11 Oct | Indigenous Peoples Day (holiday) |
| 15 | 13 Oct | Integral morphisms | 4.2 |
| 16 | 15 Oct | Normalization | 4.3-4.4 |
|
| 17 | 18 Oct | Krull's dimension | 4.5 |
| 18 | 20 Oct | Chevalley’s finiteness theorem | 4.6 |
| 19 | 22 Oct | Valuations and smooth curves | 5.1-5.2 |
|
| 20 | 25 Oct | Constructible sets, closed sets | 5.3-5.4 |
| 21 | 27 Oct | Proper morphisms, semicontinuous functions | 5.5-5.6 |
| 22 | 29 Oct | O-modules | 6.1-6.3 |
|
| 23 | 1 Nov | The sheaf property | 6.4-6.5 |
| 24 | 3 Nov | Direct images | 6.6-6.7 |
| 25 | 5 Nov | Twisting | 6.8-6.9 |
|
| 26 | 8 Nov | Complexes and cohomology | 7.1-7.2 |
| 27 | 10 Nov | Characteristic properties of cohomology | 7.3-7.4 |
| 28 | 12 Nov | Cohomology of twisting modules | 7.5 |
|
| 29 | 15 Nov | Finiteness of cohomology | 7.6-7.7 |
| 30 | 17 Nov | Bézout's theorem | 7.8 |
| 31 | 19 Nov | Divisors | 8.1 |
|
| 32 | 22 Nov | Riemann-Roch, version 1 | 8.2 |
| 33 | 24 Nov | Birkhoff-Grothendieck theorem | 8.3 |
| 26 Nov | Thanksgiving holiday |
|
| 34 | 29 Nov | Differentials and trace | 8.4, 8.6 |
| 35 | 1 Dec | Riemann-Roch, version 2 | 8.7 |
| 36 | 3 Dec | Using Riemann-Roch | 8.8 |
|
| 37 | 6 Dec | Final project presentations | |
| 38 | 8 Dec | Final project presentations | |
