Spring 2023 - MATH 819 G100
Algebra: Selected Topics (4)
Class Number: 6503
Delivery Method: In Person
A second course in algebraic geometry, introducing students to the fundamental tools of the subject, including sheaves, schemes and cohomology.
Topics (roughly Hartshorne II.1–II.8 and III.1-III.4):
– Sheaves, ringed spaces, schemes, morphisms of schemes
– Dimension and smoothness
– Quasicoherent sheaves of modules
– Line bundles, divisors, maps to Pn
– Sheaf cohomology
– (Time permitting) vector bundles and Grassmannians
- Grades will be based on homework sets 50%
- Final exam 30%
- Final written project 20%
Homework sets will be every two weeks (6 homework sets over the term)
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the
posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester
MATERIALS + SUPPLIES:
– Algebraic Geometry, Robin Hartshorne (primary)
– The Rising Sea: Foundations of Algebraic Geometry, Ravi Vakil (secondary)
– The Geometry of Schemes, David Eisenbud and Joe Harris (secondary)
This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings,
this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable
internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in
a computer is sufficient).
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html