MMA320, Introduction to Algebraic Geometry, Spring 18

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Welcome to the course!
Graduate students are welcome, as this course is a joint MSc/PhD course.

The lectures are on Monday 10:00 - 11:45 in MVF23 and Wednesday 13:15 - 15:00 in MVH12, and the exercise session on Thursday 8:00 - 9:45 in MVH12.

The first lecture is on Monday Januari 15, 10:00 - 11:45 in MVF23. There the remaining schedule will be determined.

The schedule for the course can be found in TimeEdit.

Teachers

Course coordinator: Jan Stevens

Course literature


Lecture notes for the course.

Exercises for Chapter 1.

Exercises for Chapter 2.

Exercises for Chapter 3.

Exercises for Chapter 4.

Exercises for Chapter 5.

Exercises for Chapter 6.

Reference literature:

William Fulton, ALGEBRAIC CURVES, An Introduction to Algebraic Geometry, available from the Author's homepage.

Miles Reid, Undergraduate Algebraic Geometry. LMS Student Texts 12, Cambridge Univ. Press, 1988

Klaus Hulek, Elementary Algebraic Geometry. Student mathematical library Vol. 20, American Mathematical Society, 2003.

Program

The schedule is preliminary.

Lectures

Week
Chapter Contents
3
1
affine algebraic varieties, Nullstellensatz
4
1
irreducible coponents, regular functions
5
2
projective varieties
6
3
Bezout's theorem and the group law on a cubic curve
7
4
dimension
8
5
tangent space and nonsingularity
9
6
27 lines on a cubic surface

Recommended exercises

Week
Exercises
3
1.4, 1.5, 1.6, 1.8, 1.11, 1.13, 1.14, 1.15, 1.18, 1.22
4
1.19, 1.20, 1.21, 1.23, 1.25, 1.28, 1.29, 1.30
5
1.33, 2.1, 2.2, 2.3, 2.6, 2.14, 2.15, 2.19, 2.20, 2.21
6
2.27, 2.28, 3.2, 3.3, 3.5, 3.6, 3.13
7
3.9, 3.12, 3.16, 3.19, 3.20, 3.22, 3.27
8
4.1, 4.2, 4.4, 4.5, 4.6, 4.7, 4.8, 4.12, 4.13
9
5.2, 5.3, 5.4, 6.1, 6.2, 6.4, 6.9, 6.10

Course requirements

The learning goals of the course can be found in the course plan.

Assignments


Homework to be handed in on Wednesday Jan 24 at the latest: exercises 1.1, 1.2, 1.3 and 1.12 from Exercises for Chapter 1.

Homework to be handed in on Wednesday Jan 31 at the latest: exercises 1.31, 1.27 and 1.41.

Homework to be handed in on Wednesday Feb 7 at the latest: exercises 2.5, 2.11 (do 2.10 if necessary), 2.29.

Homework to be handed in on Wednesday Feb 14 at the latest: exercises 3.4, 3.18 , 3.23 and 3.26

Homework to be handed in on Wednesday Feb 21 at the latest: exercises 4.3, 4.6 , 4.9 and 4.13

Homework to be handed in on Wednesday Feb 28 at the latest: exercises 5.5, 5,7 and 6.6

Examination


To pass this course you should pass an oral exam.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.