Math 273 Course Webpage
Fall 2010, Duke University
General information |
Course description |
Homework assignments |
Grading policies |
Other texts |
Lecture: Tuesday and Thursday, 13:15 – 14:30, Physics Building 227
Contact information for the Instructor
Name: Prof. Ezra Miller (you should call me "Ezra")
Address: Mathematics Department,
Duke University, Box 90320,
Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Course webpage: you're already looking at it...
but it's http://math.duke.edu/~ezra/273/273.html
Office hours:Thursday, 14:30 – 16:00, Physics 209
Course content: selected from Chapters 3 &ndash 18 of [Vakil]
= Foundations of algebraic geometry, notes by Ravi Vakil
Prerequisite: A solid course on commutative algebra, including
basic notions from category theory: functors, universal properties,
exact sequences, Hom, tensor product, abelian categories, direct and
inverse limits; see [Vakil, Chapter 2], for a guide to what you might
- spectrum of a ring
- schemes (affine, projective, neither)
- types of schemes (reduced, normal, factorial, regular)
- morphisms of schemes: immersions, finiteness conditions
- quasicoherent sheaves
- fiber products
- affine and projective morphisms
- separated and proper morphisms
- line bundles
Check here two weeks before each homework is due for the
specifics of the assignments. If an assignment hasn't been posted,
and you think it should have been, then please do email me. Sometimes
I encounter problems (such as, for example, the department's servers
going down) while posting assignments; other times, I might simply
have forgotten to copy the assignment into the appropriate directory,
or to set the permissions properly.
- Tentative due dates for the homework assignments this semester
are listed in the table below. You will have approximately two
weeks to do each assignment.
- All solutions you turn in must be typewritten.
Communicating your ideas is an integral part of being a
mathematician. It is essential that you learn this skill in
graduate school. In addition to the usual PDF files, I will
provide the LaTeX source files for each of the homework
assignments. You should feel free to use (or not) these as
LaTeX templates for your solutions, by simply filling in your
responses in those files. I will be happy to answer any
questions you might have about LaTeX, although you might want
to ask your classmates first.
- Turn in your printed homework solutions to me in class, and
send electronic versions to me. Send at least your .tex
file (I may comment on your TeX usage); if you include your
.pdf file as well then it can serve as verification that your
system produces the same thing as mine does.
- Print your typed solutions double-sided. This will save
paper and lighten the stack of papers that I have to carry around.
- I encourage collaboration on homework, as long as each
person understands the solutions, writes them up using their
own words, and indicates—on the homework page—who
their collaborators were.
- You must cite sources in your solutions. If you rely on
so-and-so's theorem, then you must state the theorem and tell
me where you found it. Be specific: "the local-ringed spaces
proposition" is not precise; in contrast, "[Vakil, Proposition
7.3.1]" is. (Even better would be, "a key result on morphisms
of affine schemes as local-ringed spaces [Vakil, Proposition
7.3.1]".) Theorems are often known by many names, so I'm
likely not to recognize many theorems by names you might
- Late homework will not be accepted. Early homework is
fine: leave the hard copies in my mailbox in the Math Department.
- Homework solutions should be thoroughly explained: there will
be no credit for unsupported answers.
| Homework #1
| Tue. 14 September
| Homework #2
| Tue. 28 September
| Homework #3
| Thu. 14 October
| Homework #4
| Tue. 26 October
| Homework #5
| Tue.   9 November
| Homework #6
| Thu.   9 December
Final course grades will be entirely determined by homework and
participation. (Thus your grade may be lowered if you are absent from
|| Publisher, date
|| Algebraic Geometry, a first course
|| Springer, 1995
|| Algebraic Geometry
|| Springer, 1977
|| The Geometry of Schemes
|| Eisenbud & Harris
|| Springer, 2000
|| Principles of Algebraic Geometry
|| Griffiths & Harris
|| Wiley, 1978
University academic links
The fine print
I will do my best to keep this web page for Math 273 current, but
this web page is not intended to be a substitute for attendance.
Students are held responsible for all announcements and all course
content delivered in class.
Many thanks are due to Jeremy Martin and Vic Reiner, who provided
templates for this webpage.
The views and opinions expressed in this page are strictly those of
the page author. The contents of this page have not been reviewed or
approved by Duke University.
Mon Oct 25 23:53:00 EDT 2010
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