The Hilbert scheme of points on singular surfaces.

Xudong Zheng , Johns Hopkins
Fine Hall 322

The Hilbert scheme of points on a quasi-projective variety parametrizes its zero-dimensional subschemes. When the variety is a singular surface, the geometry of the Hilbert scheme reflects the singularity of the underlying surface. I will present some work in progress on the Hilbert schemes of points on surfaces of embedding dimension three and four. Part of the talk will be on a joint work with Lawrence Ein.