Math 627 Course Webpage
Algebraic Geometry
Fall 2022, Duke University
General information |
Course description |
Homework assignments |
Grading policies |
Other texts |
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Lecture: Tuesday and Thursday, 13:45 – 15:00, 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
Email: ezra
math.duke.edu
Webpage:
https://math.duke.edu/people/ezra-miller
Course webpage: you're already looking at it...
but it's http://math.duke.edu/~ezra/627/627.html
Office hours: Tuesday and Thursday, 12:45 – 13:45, Physics 209
Course content: selected from Chapters 2 – 17 of [Vakil]
=
Foundations of algebraic geometry, notes by Ravi Vakil,
dated November 18, 2017
- sheaves
- 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
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 1] for a guide to what you might
need.
- 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 using the
LaTeX templates provided for each of the homework assignments.
Communicating your ideas is an integral part of being a
mathematician. It is essential that you learn this skill in
graduate school. Simply fill your responses into the provided
LaTeX files; the formatting and macros in the preamble are
designed to enable grading, and altering those would disable
their functionality. I will be happy to answer any questions
you might have about LaTeX, although you should ask your
classmates first.
- Turn in your homework solutions by sending electronic
versions to me. Send your .tex file (I may comment on your
LaTeX usage) and include your .pdf file as verification that
your system produces the same thing as mine does.
- Do not print your solutions. This will save paper. I
will not read or otherwise use the printed version anyway.
- I encourage collaboration on homework, but
- Each student must write their own solutions using their own
words, and
- Indicate—on the homework page—who your
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 can be known by many names or designations,
so I'm likely not to recognize many theorems by names you might
attach.
- Late homework will not be accepted. Early homework is
fine.
- Homework solutions should be thoroughly explained: there will
be no credit for unsupported answers.
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, my own internet or 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.