Math 6175 (Fall 2024):
Algebraic Geometry II
About this course
Welcome to Algebrac Geometry II! This is a second-semester graduate class on algebraic geometry, following Hartshorne's text. The core topics are schemes and the cohomology of coherent sheaves. If there is time, we will discuss algebraic curves from the schematic perspective. Recommended (but not required) prerequisites: commutative algebra (Math 6150), homological algebra (Math 6290), and a first course in algebraic geometry (Math 6170).
Contact information
- Instructor: Jonathan Wise
- Office: Math 204
- E-mail: jonathan.wise@colorado.edu
- Phone: 303 492 3018
You may also contact me anonymously.
Office hours
My office is Room 204 in the Math Department. My office hours sometimes change, so I maintain a calendar showing the times I will be available. You can also make an appointment or drop in without an appointment.
Syllabus and textbook
Our main textbook:
R. Hartshorne, Algebraic Geometry.
The following book is very good for independent study:
R. Vakil, The Rising Sea.
Course goals
The goal is to become comfortable enough with the modern language of algebraic geometry to read papers and advanced textbooks that use it. You should come out of this class ready to read a book like Fulton's Intersection Theory or Mumford's Abelian Varieties.
Homework and grading
Grades will be based on in-class presentations of exercises and topics from the text. All students who participate regularly in these assignments will receive an 'A'. Students taking the class pass/fail should discuss expectations with me privately.
There will also be regular assignments of mechanical problems that are necessary for understanding, but which will not be collected.
Feedback
Special accommodations, CoViD-19, classroom behavior, and the honor code
The Office of Academic Affairs officially recommends a number of statements for course syllabi, all of which are supported in this class.
If you need special accommodation of any kind in this class, or are uncomfortable in the class for any reason, please contact me and I will do my best to remedy the situation. You may contact me in person, by e-mail, or anonymously.