MATH 431 Algebraic Geometry
Spring 2014
Ali
Sinan Sertöz
Faculty
of Science, Department of Mathematics, Room: SA-121, Phone 1490.
Office Hours: Monday 10:30-12:00
What is MATH 431 (2014) |
What is MATH 431 (2012) |
What is MATH 431 (2011) |
Textbook:
Hartshorne, Algebraic Geometry,
Springer-Verlag GTM Vol 52, (1977).
(First chapter only for most of the topics we will cover.)
Recommended Textbooks:
Griffiths and Harris, Principles of Algebraic Geometry, Wiley-Interscience, (1978).
Shafarevich, Basic Algebraic Geometry, Springer-Verlag, (1977).
Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, (1985)
I will provide copies of some simple articles for some of the material in class.
Most importantly I will distribute lecture notes which will eventually become a book at the end of the semester.
Syllabus:
Week |
Date |
Subjects to be covered | Class Hours |
0 | Feb 5 | Motivation | 2 |
1 | Feb 10-Feb 12 | Affine varieties | 4 |
2 | Feb 17-Feb 19 | No Class This Week | 0 |
3 | Feb 24-Feb 26 | Affine morphisms | 4 |
4 | Mar 3-Mar 5 | Affine complete intersections | 4 |
5 | Mar 10-Mar 12 | Projective varieties | 3 |
6 | Mar 17-Mar 19 | Projective morphisms | 3 |
7 | Mar 24-Mar 26 | Smooth vs singular | 3 |
8 | Mar 31-Apr 2 | Arf rings | 3 |
9 | Apr 7-Apr 9 | Affine toric varieties | 3 |
10 | Apr 14-Apr 16 | Projective toric varieties | 3 |
11 | Apr 21 | Grassmannians | 1 |
12 | Apr 28-Apr 30 | Grassmannians | 3 |
13 | May 5-May 7 | Curves | 3 |
14 | May 12-May 14 | Riemann-Roch | 3 |
Total=42 | |||
This syllabus is tentative. We may spend more time than allocated on a topic if the class is interested in the subject or if the class finds the pace fast. So we may not cover everything mentioned above. However the bare bones of the course are affine varieties, projective varieties, toric varieties and Arf rings. We will definitely cover them in detail to everybody's satisfaction. |
Schedule:
MON | 09:40-10:30 | SA-Z01 |
WED | 10:40-12:30 | SA-Z01 |
On February 10, February 24 and March 3 we will start our Monday class at 8:30 to compensate for the 3 lost hours of week 2. |
Exams and Grading:
By Yönetmelik
Madde 4.7 here is our FZ grade policy:
Failure
to attend at least 50% of the classes or averaging
less than 40% from the two midterms will result in an FZ grade.
Midterm 1-Takehome | 25% | Given on March 5 Wednesday |
Due on March 10 Monday |
Solutions |
Midterm 2-Takehome |
25% |
Given on April 16 Wednesday | Due on April 21 Monday | Solutions |
Final-Takehome | 25% | Given on 26 May 2014, at 9:00 | Due 26 May 2014, at 17:30 | Solutions |
Homework | 20% | |||
Attendance |
5% |
|||
Homework 1 | Due date: 24 Feb 2014 | Homework 1-Solutions | ||
Homework 2 | Due date: 21 Apr 2014 | Homework 2-Solutions |
The course will be graded according to the following catalogue:
[0,39] | F |
[40,44] | D |
[45,49] | D+ |
[50,53] | C- |
[54,56] | C |
[57,59] | C+ |
[60,62] | B- |
[63,65] | B |
[66,68] | B+ |
[69,71] | A- |
[72,100] | A |
Old Exams:
You can refer to my all courses page. However I have never given two similar Math 431 courses in the past. All are different as is this one.