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: 10-11 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 Donaldson-Thomas theory) gives new phenomenon to look at the Hilbert schemes. If time permits, we will introduce the basic notion of Donaldson-Thomas theory and the interesting role of Hilbert schemes in the theory. This course is a second start up for Algebraic Geometry, and also a warm-up for the research area on Gromov-Witten theory and Donaldson-Thomas 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

• Here are the homework assignments.

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.