3:45: Hilbert Scheme of PointsDustin CartwrightHilbn(X) parametrizes 0-dimensional, degree n subschemes of X. Even for X equal to affine or projective space over an algebraically closed field, Hilbn(X) can be quite complicated. Much research has been done on the case of smooth surfaces, for which Hilbn(X) is well-behaved, and in particular smooth. However, while it is known that higher dimensional cases are more complicated, even basic questions are open, such as the irreducibility of Hilbn(A3) for many values of n. I will introduce the Hilbert schemes of points, and then present examples illustrating the complex behavior that is possible. |
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