| Date | Topic | Book | Homework | |
|---|---|---|---|---|
| Jan. | 7 | What is algebraic geometry? | ||
| 8 | Shapes, functions and pullbacks | |||
| 10 | Faithfullness of pullbacks | |||
| 14 | Affine algebraic varieties | §1.2 | ||
| 15 | Computing in quotient rings | H1 | ||
| 17 | Morphisms of affine varieties | A1 | ||
| 21 | More on morphisms | |||
| 22 | Categories, functors, and isomorphisms | H2 | ||
| 24 | Discussion of projects | A2 | ||
| 28 | Ideals and radicals | |||
| 29 | Maximal ideals in quotient rings | H3 | ||
| 31 | The Nullstellensatz | §4.1 | A3 | |
| Feb. | 4 | The ideal/subvariety correspondence | §4.2 | |
| 5 | Chain conditions | H4 | ||
| 7 | The Zariski topology | §4.4 | A4 | |
| 11 | More on the Zariski topology | |||
| 12 | Principal open sets | H5 | ||
| 14 | Functions and patching | A5 | ||
| 18 | ||||
| 19 | Reading Week | |||
| 21 | ||||
| 25 | Sheaves of functions | |||
| 26 | Projective Space | §8.2 | H6 | |
| 28 | More about P2 | A6 | ||
| Mar. | 4 | Homogeneous polynomials | ||
| 5 | Homogenization and dehomogenization | H7 | ||
| 7 | Projective varieties | §8.2 | A7 | |
| 11 | Cones; singularities of hypersurfaces | |||
| 12 | Geometry of plane curve singularities | H8 | ||
| 14 | The genus of degree d plane curves I | A8 | ||
| 18 | The genus of degree d plane curves II | |||
| 19 | Maps between Riemann surfaces | H9 | ||
| 21 | The topology of maps between Riemann surfaces I | A9 | ||
| 25 | The topology of maps between Riemann surfaces II | |||
| 26 | The Riemann-Hurwitz formula | H10 | ||
| 28 | Consequences of the Riemann-Hurwitz formula | A10 | ||
| Apr. | 1 | The group law on an elliptic curve | ||
| 2 | A theorem of Poncelet | H11 | ||
| 4 | Polynomial solutions to polynomial equations | A11 | ||
| 8 | ||||
| 9 | H12 | |||
| 11 | A12 |