MATH 591
Algebraic Geometry
Spring 2016
Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121,
Phone: 1490
Office Hours: Tuesday 10:40-12:00 or by appointment
Textbook: Hartshorne, Algebraic Geometry,
Springer-Verlag, 1977.
Schedule:
TUE 09:40-10:30 SBZ-11
THU 10:40-12:30 SBZ-11
How will the course run and how will it be graded:
One week I will explain the main ideas in a section and then
the next week we will attack the exercises in the book.
Hartshorne's book is famous, or notorious, for the difficulty of
its exercises. For this reason there are numerous alleged
solutions floating on internet, mostly wrong!
After we solve some exercises and discuss the others I will assign
some of the discussed but not solved exercises as homework or
midterm exam depending on the complexity of the exercise.
You may choose your own homework or midterm exam exercise yourself
after consulting with me.
Overall I expect to collect, during the 15 week semester, 2
midterm exams and 4 homework problems. That makes one written and
submitted work for every other week. The final exam will be again
one particularly involved exercise of your own choice and of my
approval.
Actual grading occurred as follows:
Written Work 1:
a) Exercises I.3.7 page 21
b) On top of page 32 Hartshorne says "One can show easily that
this definition of nonsingularity is independent of the set of
generators of the ideal of Y chosen." Prove this claim.
Written Work 2:
Everybody chose and solved one exercise which interested them the
most.
Written Work 3:
Exercise I.3.20(a) page 23.
Take-home Final Exam:
a) Exercise 7.1 page 54
b) Exercise 7.2 page 54.
Almost all of the above exercises plus a lot more are solved
and discussed in class during the "Exercises" weeks, see the
syllabus below.
Solutions: Work 1
Work 2, 3 and
Final
Active class participation and regular handing in of written work
will be recognized as a sign of achievement at the time of letter
grading.
Attendance:
Attendance is essential for learning. I will take attendance
to check, at the end of the semester, if the previous sentence is
true! ☺
SYLLABUS
| Date |
Hours |
Topics |
Section |
| 28 January 2016 |
2
|
Affine Varieties |
1 |
2-4 February 2016
|
3
|
Exercises
|
1
|
9-11 February 2016
|
3
|
Pojective Varieties
|
2
|
16-18 February 2016
|
3
|
Exercises
|
2
|
23-25 February 2016
|
3
|
Morphisms
|
3
|
1-3 March 2016
|
3
|
Exercises
|
3
|
8-10 March 2016
|
3
|
Rational Maps
|
4
|
15-17 March 2016
|
3
|
Exercises |
4
|
22-24 March 2016
|
3
|
Non-singular Varieties
|
5
|
29-31 March 2016
|
3
|
Exercises |
5
|
5-7 April 2016
|
3
|
Non-singular Curves
|
6
|
12-14 April 2016
|
3
|
Exercises |
6
|
19-21 April 2016
|
3
|
Intersections in Projective Space
|
7
|
26-28 April 2016
|
3
|
Exercises |
7
|
3 May 2016
|
1
|
What to expect in MATH 592
|
8
|
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