MMA320 H22 Inledning till algebraisk geometri
This page contains the program of the course: lectures, exercise sessions, homework and computer labs. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The first lecture is on Monday, Oct 31, 10:00 - 11:45 in MVH12. Starting from Nov 1 the
lectures are on Monday 15:15 - 17:00 and Tuesday 8:00 - 9:45 and exercise sessions on
Friday 13:15 - 15:00, all in room MVF21.
The schedule of the course can be found in TimeEdit.
Lectures
The schedule is preliminary.
| Week | Chapter | Content |
|---|---|---|
| 44 | 1 | affine algebraic varieties, standard bases, resultant |
| 45 | 1 | Nullstellensatz, irreducible components, regular functions |
| 46 | 2, 3 | projective varieties, Bezout's theorem |
| 47 | 3,4 | the group law on a cubic curve, integral extensions |
| 48 | 4 | dimension, Noether normalisation |
| 49 | 5 | tangent space and nonsingularity |
| 50 | 6 | 27 lines on a cubic surface |
Recommended exercises
| Week | Exercises | |
|---|---|---|
| 44 | 1.1, 1.5, 1.6, 1.8, 1.11, 1.13, 1.14, 1.18, 1.22 | |
| 45 | 1.19, 1.20, 1.21, 1.23, 1.25, 1.28, 1.29, 1.30, 1.33 | |
| 46 | 2.1, 2.2, 2.3, 2.6, 2.11, 2.14, 2.19, 2.20, 2.21, 2.27, 2.28 | |
| 47 | 2.27, 2.28, 3.6, 3.12, 3.13, 3.16, 3.19, 3.20, 3.22, 3.27 | |
| 48 | 3.27, 4.1, 4.2, 4.4, 4.5, 4.6, 4.10, 4.12 | |
| 49 | 5.2, 5.3, 5.4, 5.6, 5.9 | |
| 50 | 6.1, 6.2, 6.4, 6.5, 6.7, 6.8 |
Homework
You can hand in in any format. You can e.g. scan handwritten solutions.
Computer labs
There will be some exercises using one of the computer algebra systems Macaulay2 or Singular. You may choose. There is no need to install the program, as there is a free web-interface to Macaulay2 and to Singular. See the respective website for tutorials.
An introduction to computations with Macaulay2 and Singular will be posted soon here.
Course summary:
| Date | Details | Due |
|---|---|---|