Instructor — Roi Docampo (roi@ou.edu)

Meeting — MWF 1:30–2:20, PHSC 809.

Course Description — This course serves as a first introduction to Algebraic Geometry. This is a central subject in modern mathematics, with close connections with number theory, representation theory, differential geometry, and combinatorics. The main objective in this course is to introduce and study basic properties of affine and projective algebraic varieties. A special emphasis will be put on concrete geometric examples. At the same time, we will develop all of the Commutative Algebra needed to understand the material.

Lecture Notes — We will mainly follow the lecture notes on the subject written by Andreas Gathmann. We will be using the latest version (last updated on April 29, 2017). You can download a copy on the author's website, or directly here:

Lecture_Notes_in_Algebraic_Geometry_by_Andreas_Grathman.pdf.

Additional References — In addition to the above lecture notes, occasionally we will also draw on other sources. The most relevant among them are:

Igor Shafarevich, Basic Algebraic Geometry I, Varieties in Projective Space.
William Fulton, Algebraic Curves.
Joe Harris, Algebraic Geometry: a first course.
Olivier Debarre, Introduction to Algebraic Geometry (course notes, in French).
David Mumford, Algebraic Geometry I, Complex Projective Varieties.

Commutative Algebra References — As mentioned above, during the course we will develop the notions of Commutative Algebra that are needed to understand the material. For more details on this subject, the standard references are:

Michael Atiyah and Ian G. MacDonald, Introduction to Commutative Algebra.
Hideyuk Matsumura, Commutative Algebra.
David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry.

Advanced Algebraic Geometry References — The following is a list of more advanced references. You might wish to consult them for more in depth treatments of the subject.

Robin Hartshorne, Algebraic Geometry.
David Mumford, The red book of varieties and schemes.
Phillip Griffiths and Joe Harris, Principles of Algebraic Geometry.
The Stacks Project.
EGA and SGA.

Algebraic Geometry and Commutative Algebra