Math 996 Fall 2018, Hilbert Schemes
Course Information

Time: MW 11:00 12:15 PM

Location: Snow Hall 564

Text: No textbook required. I will mainly follow my notes. You can find many text books and notes online on Hilbert schemes, for instance, Nakajima's book
The Hilbert schemes of points on the surfaces, and Lehn's book "Hilbert scheme of points on surfaces".
 Instructor: Dr. Yunfeng Jiang
 Office: Snow Hall 625
 Email: y.jiang@ku.edu
 Office Hour: M, W, F: 1011 AM or by appointment.
 Course Coverage: The course of "Toric on Hilbert schemes" intends to cover the basic materials of Hilbert schemes. The Hilbert schemes are
a very important and interesting schemes in algebraic geometry. We begin the functor point of view on Hilbert schemes, talk about the basic notions
and properties of Hilbert schemes, and finally pay more attention on the Hilbert scheme of points on surfaces and threefolds.
The recent development on enumerative geometry (especially on DonaldsonThomas theory) gives new phenomenon to look at the Hilbert schemes. If time
permits, we will
introduce the basic notion of DonaldsonThomas theory and the interesting role of Hilbert schemes in the theory.
This course is a second start up for Algebraic Geometry, and also a warmup for the research area on GromovWitten theory and
DonaldsonThomas theory in modern enumerative algebraic geometry.
Grade Policy
 Homework: Homework will be assigned occasionally.
 Midterm Exam: There will be no midterm.
 Final Exam: There will be no Final exam, but a project for each student at the end of the semester.
 Grade Percentage: homework (50 %) + final project (50 %).
Homework
Accommodation
 If you have a
disability and need some kind of accommodation, please contact
Dr. Yunfeng Jiang at the start of the semester so the necessary
arrangements can be made.