Math 582 Graded Rings and Geometry (Winter 2006)

Office Hours: Wednesday, Friday 3:30-4:30 in Padelford C-418, and by appointment.

The course: A description of the course can be found here. There is no single book that covers the material in the course but I have put some books on Reserve at the library:

N. Popescu, Abelian categories with applications to rings and modules, Chapter 3 on Localization and quotient categories
E. Miller and B. Sturmfels, Combinatorial commutative algebra, Chapters 8,10,11,13 on graded rings and toric varieties
M.P. Brodmann and R.Y. Sharp, Local cohomology : an algebraic introduction with geometric applications

I am wrting notes for the course which will be posted here periodically. I would appreciate any feedback and/or criticism, either major or minor.

Homework and grades.

I will assign individualized HW exercises that are taken from either Fulton's book or the list of homework exercises I posted here. You may submit a solution to any problem, but you MUST submit one for those assigned to you. You are also required to review others' submitted solutions. You are also required to submit a final version at the end of the quarter incorporating all reasonable suggestions and corrections given in reviews or by me for all HW problems assigned to you. Some problems will be assigned to more than one person. You are welcome to collaborate and submit the same solution.

For "normal progress", you MUST submit SOLUTIONs to the problems assigned to you and at least two REVIEWs of someone else's work per week. If you submit a SOLUTION to a regular problem, you will receive 3 points. If you submit a SOLUTION to a problem with an asterisk, you will receive 5 points. If your solution is reviewed by someone and found correct, you will receive 2 extra points. You cannot review your own work. If it is reviewed and found incorrect you will lose some points based on how serious the error is. To write a REVIEW, you have to decide whether the solution is correct or not and be able to support your opinion. The first (submitted) REVIEW of any solution is worth 1-3 points if correct. However you lose 1 point if you say a solution is good when it is not (in other words you get -1 for the review). You may submit a review for a solution that has been reviewed only if the first review is less than a day old. The second review of the same solution is worth 1-2 points, the third is worth 1 point and any subsequent one will have only intellectual value. However, if you disagree with a submitted review, you may submit a "competing" review at any time.

Submitting sloutions and reviews via EPost to the Message Board. If you are submitting a
SOLUTION put "solution #" in the subject field where # is the number of the problem on the HW list.
REVIEW use the "reply to message" option so your review will be linked to the reviewed solution.

In either case you should submit things in (La)TeX by either:
- Creating a pdf (or dvi, or ps) file of your submission, and attaching the file to your posting. PDF is probably best.
- Or posting it on your own webpage and submitting the URL to the EPost site.
Here are Sandor's LaTeX style file and sample for HW submission.