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Title:
On the local geometry of Hilbert Schemes
Speaker:
Abstract:
In the talk we examine the local geometry of the Hilbert Scheme of $d$ points on $\mathbb{P}^n$. If $n > 2$ little is known about the dimension of this scheme and its local properties. After reviewing some classical results on connectedness and smoothness, we concentrate on irreducibility of the Hilbert Scheme and explore the rich interplay between the properties of the algebra corresponding to a point $p$ of the Hilbert Scheme and the local geometry of this scheme near $p$.
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