12/25/17: Happy Holidays to all and thank you for a great semester of
group study! I am moving things to a new course page for the Spring
Semester:
http://www-users.math.umn.edu/~voronov/8254-18/. The first
homework of the Spring Term will be posted there soon.
12/1/17, 3 a.m.: Homework 5 is posted on the class web site with a due
date of Monday, December 11.
11/29/17: I have not been able to work much on the next homework
today, unfortunately. I plan to post it on Thursday and make it due on
Monday, December 11.
11/29/17: As I wrote to you in a message today, I got sick and had to
cancel today's class meeting and make it up on Friday, regular time,
3:35-4:50, regular classroom. I am recovering and should be okay by
then. Just in case, I would also like to reschedule my tomorrow's
office hours 11:15-12:05 to same time on Friday.
11/20/17: I will be out of town on pre-Thanksgiving Wednesday: no
office hours. See me during my office hours on another day or make an
appointment, if you would like to see me.
11/15/17: It does not look like it will make sense to hold the class
meeting on Wednesday evening before Thanksgiving, November 22. Thus, I
would like to cancel it. Have a great holiday!
11/13/17: Since I had a few requests for turning homework late, I have
decided to extend the deadline for this HW till Wednesday.
11/8/17: I have added the word closed to Problem 5 on Homework
4. Otherwise, the second part of the problem does not work. Thanks to
Xinchen Miao who pointed this out to me!
11/5/17: Homework 4 is posted on the class web site with a due date of
Monday, November 13.
10/22/17: Homework 3 is posted on the class web site with a due date
of Monday, October 30.
10/16/17: There is a workshop on Algebraic Geometry at Harvard in
February 2018 specifically for graduate students in the early years,
see https://sites.google.com/view/gwag/. They
have some financial support for attanedance available. The application
deadline is November 13, 2017.
10/9/17: I have corrected Problem 2 on Homework 2 and changed the due
date to Monday, October 16.
10/5/17: Homework 2 is posted on the class web site with a due date of
Wednesday, October 11.
9/26/17: Craig Westerland has asked me to substitute for him in his
1:25-2:15 class next week. Because of that, I have to move my
Wednesday, October 4, office hours to 2:30-3:20, just for that day.
9/26/17: I have expanded the hint I gave in class yesterday to Problem
8 in a new version of the homework. Reload the web page, if you do not
see the hint.
9/20/17: I have corrected Problem 7 on the homework. Now this problem
contains an optional challenge question, which you may safely skip,
unless you need some food for thought.
9/20/17: Things in class have been going slower than I thought they
would, and I am moving the due date of Homework 1 up again. Now it is
due on Wednesday, September 27.
9/17/17: Because of a Topology Seminar meeting scheduled at irregular
time this Monday, I would like to move my Monday, September 18, office
hours to start at 1:25 p.m. For the rest of the term, they will remain
to begin at 2:30 on Mondays.
9/13/17: One minor correction to today's class. The way I worded an
equivalence
{Affine varieties over k} → {Finitely
presentable integral domains over k},
V ↦ O(V),
where an affine variety V
was a polynomial system with the defining ideal being prime, was quite
obvious, based on what we had done, if you recall the definition of a
prime ideal. However, usually, when talking about varieties, one
really does not mean the point functor, but rather the actual solution
set just in kn, and O(V) does not mean
k[t_1, ..., t_n]/(f_1, ..., f_r), but rather the algebra of
functions on the solution set, as you identify those functions whose
values on all the k-points agree. This means O(V)
= k[t_1, ..., t_n]/rad(f_1, ..., f_r), where rad is the
nilradical of the ideal, and then you need a version of Hilbert's
Nullstellensatz to prove the equivalence theorem.
9/12/17: I would like to move my Friday office hours to Thursday
11:15-12:05 for the rest of the term. Now my office hours are: M
2:30-3:20, W 1:25-2:15, Th 11:15-12:05. Remember, I always happy to
see you!
9/12/17: Having made the first homework, I have decided it would be
wise to move the due date up again. Now Homework 1 is posted on the
class web site with a due date of Monday, September 25.
9/11/17: As Lucy Yang pointed out, my Step 3 of the proof of today's
main theorem on the equivalence of categories did not prove what we
wanted to prove. Sorry: I gave one trivial argument instead of
another. Here is a correction. We need to show that every finitely
presented k-algebra k' is isomorphic to O(V) for
some polynomial system V. Well, a finitely presented algebra has a
finite number of generators, say, t1,
..., tn, and a finite number of defining relations,
say, f1, ..., fr. Then for the
system V defined by f1 = 0 ,
..., fr = 0, we have O(V) ≅ k'.
9/11/17: On the popular request, I am changing the time and room for
Math 8253 Algebraic Geometry, effective today:
Time: Monday, Wednesday 3:35-4:50
Room: Mechanical Engineering 102
9/8/17: It looks like everybody agrees to change the class schedule
from MWF 3:35-4:25 to MW 3:35-4:50. I have asked Stephanie to find a
new room for our class, as our room has the next class starting at
4:40. As soon as I hear from her, I will implement the change. For the
time being, assume that we are on the old MWF schedule.
9/8/17: I am changing the date of the first homework due to
Wednesday, September 20. Because of Tschinkel's talk, we will not
study enough material before the original date of September 15.
9/8/17: Today's class is canceled, as I communicated, hopefully, to
all of you by e-mail early this morning. For those who have not
received that message, here is what is going on. I found out that the
prominent algebraic geometer Yuri Tschinkel of Courant Institute, New
York University, will be here this weekend for personal matters,
arriving today, Friday, early afternoon. We have a great opportunity
to catch him for a seminar talk. Since the only time he is available
to give a talk is during our class meeting slot, I have decided to
schedule his talk for 3:35-4:25 in our classroom, Folwell Hall 121.
You do not have to, but I encourage you to gather your courage and attend his talk, even though there is a good chance you will not understand a word, as he will be talking about rational varieties in the spirit of https://arxiv.org/abs/1503.08497. In general, it is a good idea to attend occasional research talks in the subjects you are studying.
Here is more information about the talk:
Venue: Special Algebraic Geometry & Lie Theory Seminar
Title:
Rationality Problems
Abstract: I will discuss recent advances in
the study of rationality properties of higher-dimensional algebraic
varieties (joint work with B. Hassett, A. Kresch and
A. Pirutka).
Speaker: Yuri Tschinkel (Courant Institute,
NYU)
Time: 3:35-4:25 p.m., Friday, September 8, 2017
Place: Folwell Hall 121
9/8/17: I have started writing Class Outlines, see the course web
page. I am still working on the first homework.
9/8/17: I recommend the following way to study for this class. Attend
each class, take notes, participate in class actively. After each
class review your notes and study the corresponding part of the
text. You can find out which part of the text at the Class Outlines
page. Then do the assigned homework problems pertinent to that
material. Some students find it helpful to read the material before it
is covered in class, some prefer to do the reading after class.
9/8/17: If you need to register for this course, please, send a
message to Stephanie Lawson at ugrad@math.umn.edu and ask for a permission number. If
permission is granted, go to OneStop and register.
Last modified: (2018-01-08 23:29:48 CST)