Introduction
Algebraic geometry studies 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. This course complements the department's other
offerings in algebraic geometry, and even previous incarnations of
M672.
Topics
A representative, but not definitive, sketch of topics:
- Affine varieties (varieties and ideals, coordinate rings
and morphisms...)
- Local study (tangent space, smooth and singular points...)
- Projective varieties (relation to affine, normalization
and elimination..)
- Curves and divisors
- Intersection theory
Logistics
- Time MWF 3:00-3:50 ENGRG E206
- Textbook None required, some suggested:
Requirements
Homework will be assigned weekly, and is due at the beginning of class
on Wednesdays. You're encouraged to work with other students in the
class, but the work you actually turn in must be your own. 85% of
your grade is based on your written homework.
There will be sporadic problem sessions throughout the semester,
approximately once per month. You are expected to present solutions
at least twice. 15% of your grade is based on this component.
Help
Questions directed to
j.achter@colostate.edu
will be answered swiftly. Office hours will be posted soon.
This page is available at http://www.math.colostate.edu/~achter/672