Special Topics (Fall 2018): Hilbert Schemes
Advanced courses on special topics; given as need arises.
Lectures on Hilbert Schemes of Points on Surfaces, Nakajima, American Mathematical Society, 1999.
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.
(Jiang 2018 )