The lecture follows very closely the lecture notes by Andreas Gathmann. In particular it covers
Properties of commutative rings and modules over them (as covered by the lecture Commutative Algebra).
The lecture is offered in a flipped classroom setup:
Since the format of the course is pretty new, I am always happy for feedback! You can submit it either via email or via this (anonymous) form.
You find the lecture videos on youtube.
| Week | Material |
|---|---|
| 1 | 01.01 Affine varieties - 02.03 Irreducible affine varieties |
| 2 | 02.04 Noetherian spaces and irreducible decompositions - 02.09 Dimension theory of reducible spaces |
| 3 | 03.01 Definition of regular functions - 04.02 Properties of morphisms of ringed spaces |
| 4 | 04.03 Morphisms between affine varieties - 05.05 Products of prevarieties |
| 5 | 05.06 Separatedness and the definition of varieties - 06.11 The projective closure |
| 6 | 06.12 Projective hypersurfaces - 07.06 Complete varieties |
| 7 | 07.07 The Veronese embedding - 09.01 Rational and birational maps |
| 8 | 09.02 Rational functions - 09.08 Blowing up to remove indeterminacies of rational maps |
| 9 | 10.01 The tangent space to a variety - 11.01 The lines on the Fermat cubic surface |
| 10 | 11.02 The moduli space of smooth cubic surfaces - 12.05 Regular functions and the structure sheaf of affine schemes |
The new exercises will be posted here on Fridays. We expect you to look at the problems over the weekend and to prepare questions for the exercise class on Monday.
Please hand in your solutions by the following Friday at 12:00 in your assistant's box in HG J68. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.
| exercise sheet | due by | solutions |
|---|---|---|
| Exercise sheet 1 | February 23 | Solution 1 |
| Exercise sheet 2 | March 1 | Solution 2 |
| Exercise sheet 3 | March 8 | Solution 3 |
| Exercise sheet 4 | March 15 | Solution 4 |
| Exercise sheet 5 | March 22 | Solution 5 |
| Exercise sheet 6 | March 29 | Solution 6 |
| Exercise sheet 7 | April 12 | Solution 7 |
| Exercise sheet 8 | April 19 | Solution 8 |
| Exercise sheet 9 | April 26 | Solution 9 |
| Exercise sheet 10 | May 3 |
| live problem sheet | date | solutions |
|---|---|---|
| Sheet 1 | February 27 | Solution 1 |
| Sheet 2 | March 5 | Solution 2 |
| Sheet 3 | March 12 | Solution 3 |
| Sheet 4 | March 19 | Solution 4 |
| Sheet 5 | March 26 | Solution 5 |
| Sheet 6 | April 9 | Solution 6 |
| Sheet 7 | April 16 | Solution 7 |
| Sheet 8 | April 23 | Solution 8 |
| Sheet 9 | April 30 |
| time | room | assistant | language |
|---|---|---|---|
| Mo 16-17 | HG E 1.2 | Dmitrii Krekov | English |