Introduction to Algebraic Geometry - Fall 2015
Monday, Wednesday, Friday 12:50 pm - 1:40 pm, Hayes Healy 125
Course website:
nd.edu/~smapes1/algebraicGeometry.html
Instructor:
Sonja Mapes
Email:
smapes1 (at) nd.edu
Office: 228 (Hayes-Healey)
Tel: (574) 631-7586
Office hours:
TBA
Or by appointment.
Textbook:
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
Grading:
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.
Honesty:
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
www.honorcode.nd.edu .
Syllabus
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 |