Introduction to Algebraic Geometry - Fall 2015

Monday, Wednesday, Friday 12:50 pm - 1:40 pm, Hayes Healy 125
Course website:


Sonja Mapes
Email: smapes1 (at)
Office: 228 (Hayes-Healey)
Tel: (574) 631-7586

Office hours:

Or by appointment.


We will roughly follow the Algebraic Geometry notes by Andreas Gathmann. The notes can be be found here .

Some other resources (which will hopefully be on hold in the library) are:
Algebraic Geometry by Hartshorne
Geometry of Schemes by Eisenbud and Harris
Algebraic Geometry (A First Course) by Harris
Invitation to Algebraic Geometry by Smith, Kahanpaa, Kekalainen, and Traves
Computational Algebraic Geometry by Schenck


There will be 4 or 5 homework assignments. The grade will be based on class attendance and the homework.

Other resources:

I hope to make use of the computer algebra system Macaulay2 in this course. If you have a mac or a linux machine I strongly encourage you to install it along with some form of emacs on your own computer. If you are using windows, you can also install it but I will not be able to offer much support for it (at least interfacing with emacs). For information on how to download and install Macaulay2 go here. Alternatively you can use Macaulay2 in a web browser by going to this website.


This class follows the binding Code of Honor at Notre Dame. The graded work you do in this class must be your own. In the case where you collaborate on homework with other students make sure to fairly attribute their contribution to your project. For more information on the honor code see .


This is a tentative syllabus and it is likely to change as the course progresses.

Date Reading - sections in textbook
Aug. 26,28 What is Algebraic Geometry, Commutative Algebra odds and ends
Aug. 31, Sept. 2,4 Affine Varieties
sec. 1.1-1.3
Sept. 7,9,11 Affine Varieties, Morphisms
sec. 1.4, 2.1
Sept. 14,16,18 Affine Varieties
sec. 2.2, 2.3
Sept. 21,23,25 Morphisms
sec. 2.4, 2.5
Sept. 28, 30, Oct. 2 Projective Varieties
sec. 3.1, 3.2
Oct. 5,7,9 Projective Varieties
sec. 3.3, 3.4
Oct. 12,14,16 Dimension
sec 4.1, 4.2
Oct. 19,21,23 Fall break.
Oct. 26,28,30 Dimension
sec 4.3, 4.4
Nov. 2,4,6 Dimension, Schemes
sec. 4.5, 5.1, 5.2
Nov. 9,11,13 Schemes
sec. 5.3-5.5
Nov. 16,18,20 Applications of scheme theory
sec. 6.1
Nov. 23,25,27 Applications of scheme theory. Thanksgiving break (25, 27)
sec. 6.2
Nov. 30, Dec. 2, 4 Applications of scheme theory
sec 6.2, 6.3
Dec. 7,9 Applications of scheme theory
sec 6.4-6.5