Algebraic geometry studies the geometry of spaces defined by
polynomial equations. This module will study affine and projective
varieties, focusing on examples and the dictionary between algebra and
geometry. See also the description in the PYDC
| Diane Maclagan
||B1.35 Zeeman Building
|| D.Maclagan at warwick.ac.uk
||(024) 7652 8333
Course Times and Location
|| MS.03 (Zeeman building)
|| Monday 11:00-12:00
|| B3.02 (Zeeman building)
|| Wednesday 9:00 -11:00
| Support class
|| MA B3.01 (Zeeman building)
|| Tuesday, 10am in weeks 3, 4,6,8, 10
We will fairly closely follow
Introduction to Algebraic Geometry by Brendan Hassett. Also
highly recommended is
Ideals, Varieties, and algorithms, by David Cox, John Little, and
Other references you may want to consult include
Undergraduate Algebraic Geometry by Miles Reid, Algebraic Geometry by Joe Harris, and the
lecture notes of Andreas Gathmann (this contains many topics we
will not get to). Other more advanced references include the
classic by Hartshorne,
If you want to buy copies of any of these books, I recommend first
looking at a site like Alibris.co.uk,
which searches multiple independent bookstores.
There will be homework assignments every two weeks. Homework
assignments and due dates will be posted on the schedule
webpage, which will also have the reading for the following week.
You are encouraged to work on homework together, but you should write
up the solutions yourself. No late homework will be accepted. The lowest
homework score will be dropped, however, when calculating your homework mark.
Homework will be due at 12pm on the Fridays indicated on the schedule page.
In addition there will be a miniproject which will be due at the start of Term 2 (at 12pm on Tuesday, 10th January).
Your final mark for this module will depend 20% on your homework, 10%
on the mini-project, and 70% on the examination in Term 3.
There are many possible first courses in algebraic geometry, and we
cannot cover everything that might belong in such a course. In the
mini-project you will learn one of these topics, and write a five page
description of the topic at a level suitable for reading by your
classmates. The five page page-limit will be strictly enforced, and
the font must be at least 11pt.
The following is a (noncomprehensive) list of potential topics.
- Topic choice: Friday of week 4 (28th October)
- Final copy: 12pm, Tuesday, 10th January 2012.
- Bezout's theorem.
- Algebraic curves
- Abstract varieties
- Connections with complex manifolds
- Algebraic groups
- Secant varieties
- Flag varieties
- Cubic surfaces
- Rational points
- Applications to kinematics (eg Stewart-Gough platforms)
- Applications to statistics.