Introduction
Algebraic geometry uses algebra to study the geometry of systems of
polynomial equations. This innocuous description hardly hints at the
spectacular ways in which algebraic geometry blends ideas from
topology, complex analysis and combinatorics (as well as algebra and
geometry, of course). Algebraic geometry gives back to all of these
areas, and yields surprisingly concrete payoffs in number theory,
coding theory, statistics, and robotics. Even without these ancillary
benefits, algebraic geometry is a richly rewarding subject in its own
right.
This class is an introduction to affine and projective varieties over
an algebraically closed field. This is the material common to any of
the modern branches of algebraic geometry.
Logistics
The course meets MWF10-10:50 in ENGRG E204
Requirements
For much of the semester, homework will be posted weekly. It is
expected that for each problem set you will at least look at every problem, and hand in
(or be prepared to present) two problems.
Textbook
While there is no official textbook for the course, I encourage you to
consult this list of resources.
Help
Questions directed to
j.achter@colostate.edu
will be answered swiftly. Office hours will be listed here.