Homework will be
assigned weekly, due on Fridays unless announced
otherwise. Homework will be very important in this class,
and you should you work on every assigned
problem: in some cases, results developed in the homeworks may be used
in class and likewise some results may be stated without proof in class
with the proof left to you on the homework.
I encourage you to talk to other students about the homework problems,
but you must write up your own solutions and they should reflect your
If you'd like to typeset your homeworks on a computer, I would strongly
suggest learning to use LaTeχ.
The only difference between 465 and 565 is that students in Math 565
are required to typeset all of their homeworks in LaTeχ.
Please include figures in your homework write-ups whenever you think
they might be useful to the grader in understanding your
solutions. Your figures may be hand-drawn even if you are signed
up for 565.
The topic of the course is algebraic varieties (common zero sets of
polynomial equations) in affine and projective space.
Topics may include: plane algebraic curves, Hilbert's
Nullstellensatz, regular and rational maps, products of
quasi-projective varieties and the Segre embedding, completeness of
projective varieties, dimension theory, degree, Bézout's theorem,
tangent space and tangent cone, blow-ups and resolution of
singularities, Grassmannians and the Plücker embedding.
Math 463/563, or equivalent, is a prerequisite for this class:
students should be familiar with rings, fields, and Galois theory.
There will be an open-book take-home midterm and a closed-book
Homework counts as 60% of your grade. The final exam counts for
30% the midterm counts for 10%.
If you have a documented disability that will impact your work in
this class, please contact me to discuss your needs. Additionally, you
need to register with the Disability
Support Services Office in the