| 2025.01.06 |
Course overview,
Affine space
|
§1.1 |
|
| 2025.01.07 |
Affine subvarieties,
Zariski topology
|
§1.2 |
notes01 |
| 2025.01.09 |
Parametrizations,
Unirationality
|
§1.3 |
email |
| 2025.01.13 |
Ideals,
Vanishing ideals
|
§1.4 |
|
| 2025.01.14 |
Monomial ideals,
Monomial orders
|
§2.2 |
notes02 |
| 2025.01.16 |
Polynomial division,
Division algorithm
|
§2.3 |
problems1 |
| 2025.01.20 |
Hilbert basis,
Noetherian rings
|
§2.4 |
solutions1 |
| 2025.01.21 |
Projects,
Remainders
|
§2.5 |
notes03 |
| 2025.01.23 |
S-polynomials,
Buchberger criteria
|
§2.6 |
research |
| 2025.01.27 |
Buchberger algorithm,
reduced Gröbner bases
|
§2.7 |
|
| 2025.01.28 |
Macaulay2 basics,
More Macaulay2
|
§2.8 |
notes04 |
| 2025.01.30 |
Elimination,
Projections
|
§3.1 |
problems2 |
| 2025.02.03 |
Implicitization,
Classic examples
|
§3.2 |
solutions3 |
| 2025.02.04 |
Rational Implicitization,
Toric ideals
|
§3.3 |
notes05 |
| 2025.02.06 |
Common roots,
Resultants
|
§3.4 |
outline |
| 2025.02.10 |
Resultants and roots,
Properties of resultants
|
§3.5 |
|
| 2025.02.11 |
Resultants and remainders,
Resultants with many variables
|
§3.6 |
notes06 |
| 2025.02.13 |
Extension theorem (statement and proof)
|
|
problems3 |
|
Winter break |
|
|
| 2025.02.24 |
Nullstellensatz,
Radical ideals
|
§4.1 |
solutions3 |
| 2025.02.25 |
Maximal ideals,
Prime ideals
|
§4.2 |
notes07 |
| 2025.02.27 |
Sums and products,
Intersections
|
§4.3 |
draft |
| 2025.03.03 |
Closure theorem,
Colon ideals
|
§4.4 |
|
| 2025.03.04 |
Irreducible decompositions,
Primary ideals
|
§4.5 |
notes08 |
| 2025.03.06 |
Primary decompositions,
Associated primes
|
§4.6 |
problems4 |
| 2025.03.10 |
Coordinate rings,
Morphisms of affine subvarieties
|
§5.4 |
solutions4 |
| 2025.03.11 |
Homomorphisms of coordinate rings,
Dominant morphisms
|
§5.5 |
notes09 |
| 2025.03.13 |
Projective space (as a set and as a variety)
|
§8.1 |
peer feedback |
| 2025.03.17 |
Projective subvarieties,
Homogenization
|
§8.2 |
|
| 2025.03.18 |
Projective closure,
Projective nullstellensatz
|
§8.3 |
notes10 |
| 2025.03.20 |
Saturation,
Projective dictionary
|
§8.4 |
problems5 |
| 2025.03.24 |
Projective elimination,
Completeness
|
§8.5 |
solutions5 |
| 2025.03.25 |
Hilbert functions,
Hilbert polynomials
|
§9.3 |
notes11 |
| 2025.03.27 |
Multiplicities,
Finite affine subvarieties
|
§9.2 |
paper |
| 2025.03.31 |
Finite projective subvarieties,
Bézout theorem
|
§8.7 |
notes12 |
| 2025.04.01 |
Mock presentation,
Making presentations
|
§8.6 |
|
| 2025.04.03 |
Review
|
|
problems6 |
| 2025.04.?? |
Extra office hour |
|
solutions6 |
| 2025.04.11 |
|
|
video |
| 2025.04.?? |
Exam |
|
TBA |
