Hilbert scheme of points on singular surfaces

Hilbert scheme of points on singular surfaces

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Xudong Zheng , University of Illinois at Chicago
Fine Hall 322

The Hilbert scheme of points on a quasi-projective variety parameterizes its zero-dimensional subschemes. These Hilbert schemes are smooth and irreducible for smooth surfaces but will eventually become reducible for sufficiently singular surfaces. In this talk, I provide the first class of examples of singular surfaces whose Hilbert schemes of points are irreducible, namely surfaces with at worst cyclic quotient rational double points. I will also describe some consequent geometric properties of these irreducible Hilbert schemes.