Prerequisites: Math 250ABC, but please contact me if you are
interested and have not taken these courses

Textbook: Hartshorne, Algebraic Geometry, and my
lecture notes.

Syllabus: We will cover the basics of classical algebraic
geometry of affine and projective varieties defined by polynomial
equations. See also the
department syllabus.

Grading: 75% homework, 25% takehome final exam

Homework: Homework will be assigned roughly weekly

Welcome to Math 248A: Algebraic Geometry

Algebraic geometry is the study of solutions of systems of polynomial
equations. It is a classical field with a long history, which
has a close relationship to many fields of pure math, but has also recently
been applied to areas as diverse as engineering, computer
graphics, cryptography, and algebraic statistics, to name a few.
Because of the classical focus for 248A, I hope it will be accessible
to a broad audience, including applied math students.

Lecture notes

I am attempting to put together self-contained notes for the course which
could eventually replace Hartshorne. I will appreciate any feedback you
can give me on them.

Problem sets will be posted here on Wednesdays, due the following Wednesday
in class. Generally speaking, you may cite earlier exercises without proof,
but should not forward reference. If you are unsure if you should use
something, please ask. You are encouraged to collaborate with other students,
as long as you do not simply copy their answers. Beyond this, you should
not seek any external help.

There will be a takehome final exam for the course. It will be
due on December 13, by 5:00PM. Obviously,
you are not allowed to discuss it with any of your classmates or anyone
else until after you have handed it in. You may email me with questions
or concerns, but I will not give out any hints individually; if I
determine that a hint is appropriate, I will email it to everyone.