MMA320 Introduction to Algebraic Geometry Autumn 20
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 course is teached online via Zoom. The first lecture is on Monday, Nov 2, 13:15 - 15:00. After that the lectures are on Tuesday 15:15-17:00 and Wednesday 08:00-09:45, and an exercise session on Friday 15:15-17:00.
The schedule of the course in TimeEdit has vanished due to an incident with TimeEdit.
Lectures
The schedule is preliminary.
| Week | Chapter | Content |
|---|---|---|
| 45 | 1 | affine algebraic varieties, Nullstellensatz, irreducible components |
| 46 | 1, 2 | regular functions, projective varieties |
| 47 | 2, 3 | projective varieties, Bezout's theorem |
| 48 | 3,4 | the group law on a cubic curve, integral extensions |
| 49 | 4 | dimension, Noether normalisation |
| 50 | 5 | tangent space and nonsingularity |
| 51 | 6 | 27 lines on a cubic surface |
Recommended exercises
| Week | Exercises | |
|---|---|---|
| 45 | 1.5, 1.6, 1.8, 1.11, 1.13, 1.14, 1.18, 1.22 | |
| 46 | 1.19, 1.20, 1.21, 1.23, 1.25, 1.28, 1.29, 1.30, 1.33 | |
| 47 | 2.1, 2.2, 2.3, 2.6, 2.14, 2.19, 2.20, 2.21, 2.27, 2.28 | |
| 48 | 2.27, 2.28, 3.6, 3.12, 3.13, 3.16, 3.19, 3.20, 3.22, 3.27 | |
| 49 | 3.27, 4.1, 4.2, 4.4, 4.5, 4.6, 4.10, 4.12 | |
| 50 | 5.2, 5.3, 5.4, 5.6, 5.9 | |
| 51 | 6.1, 6.2, 6.4, 6.5, 6.7, 6.8 |
Homework
Exercises 1.1, 1.2, 1.4, 1.12, 1.15 due Nov 12, 17:59
Exercises 1.31 and 1.41 and the exercise on the last page of this text due Nov 19, 17:59
Exercises 2.5, 2.11 (do 2.10 if necessary), 2.29 due Nov 26, 17:59
Exercises 3.18, 3.23, 3.26 and computer exercise 3.28 due Dec 3 17:59
Exercises 4.3, 4.9 and 4.13 due Dec 10 17:59
Exercises 5.5, 5.7, 5.8 and 6.6 (exercises 5.7 and 5.8 are best done by computer) due Dec 17 17:59
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 ( or a newer interface) and to Singular. See the respective website for tutorials.
An introduction to computations with Macaulay2 and Singular
Course summary:
| Date | Details | Due |
|---|---|---|