Math 40510: Introduction to Algebraic Geometry
Spring, 2023

Instructor: Juan Migliore
Office: HAYE 236
Phone: 631-7345


Email: migliore.1@nd.edu

Office hours:
Monday 3:00-4:00 2:00-3:00,
Thursday 4:00-5:00,
Or by appointment.

Time and place of class: MWF 11:30 AM - 12:20 PM, Hayes-Healy 229.

Textbook: Ideals, varieties and algorithms, 4th Edition by David Cox, John Little and Donal O'Shea, Springer-Verlag.



Important links.

Here is the zoom link for our class. (You can click on it to get there.) The hope is that we will never need to use it!

The name of the meeting is SP23-MATH-40510-01.

Here are the notes from all of the lectures this semester. After every class I'll post that day's lecture. Until then the links will not work.

Here are the links to this semester's problem set, which I will be adding to on a regular basis. It's not in final form until I say it is!! (Make sure you always have the current version!) The links will be made active over the course of the semester.

For the purpose of review and further study, here are problem sets from the last two times I taught the class, as a useful aid to studying or for additional information.

And

Here is a practice final exam. The solutions are not written up, but please email me with any questions.

Here is another practice final exam.



Course overview: Algebraic Geometry is the study of systems of polynomial equations and their vanishing loci. This field has important components that lie in the realm of geometry, of algebra and of computation (among others) and countless applications. This course tries to give a flavor of these different aspects of the field and how they fit together. Indeed, much of the fascination of this subject comes from the myriad ways in which arguments squarely in one realm give surprising consequences that fall squarely in a different realm.

Commutative Algebra is a closely related field. This course will also be an introduction to Commutative Algebra, with an emphasis on the interplay between the two fields. We will review the basic notions from algebra (e.g. polynomial rings, ideals, quotient rings), and we will discuss the corresponding geometric objects. Gradually we will build up a Geometry-Algebra dictionary.

Here are some books that might be useful as supplemental reading. Out of courtesy to your classmates, please do not take these out for more than a few days. By far the most important reference is your textbook, but these offer interesting side reading.


Examinations, homework and grades. There will be three problem sets and a final exam. The problem sets can be accessed above. They will be updated regularly. I will let you know when the current version is in final form. Do not assume that the version you see now is in final form before I say that it is!!!

How you will be evaluated: Your course grade will be based on your total score out of 450, with points allocated as follows:

Homework and Reading: There will not be any homework assigned apart from the problem sets. In my lectures I will try to follow the material in the textbooks, although not all of it and not necessarily in the order in which it is presented there. There may also be some additional material not in the books. The problem sets will be based primarily on class lectures, but possibly also from the material in the chapters. Thus it is important to read the material as well as following the lectures.

Honor Code: Both the final exam and the problem sets are conducted under the Notre Dame Honor Code. On the first day of class I will give you a handout and I will give you very clear explanations of what is expected of you in the course and how the Honor Code applies to your work. This is important information, and if for some reason you are not in class on the first day, be sure to talk to me about it!! As always, you are strongly encouraged to come talk to me at any time if you are having any problems with anything.