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arXiv · 1407.5490

On the universal family of Hilbert schemes of points on a surface

Lei Song
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Abstract

For a smooth quasi-projective surface $X$ and an integer $n\ge 3$, we show that the universal family $Z^n$ over the Hilbert scheme $\text{Hilb}^{n}(X)$ of $n$ points has non $\mathbb{Q}$-Gorenstein, rational singularities, and that the Samuel multiplicity $\mu$ at a closed point on $Z^n$ can be computed in terms of the dimension of the socle. We also show that $\mu\le n$.

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Lei Song. 2014-07-21. On the universal family of Hilbert schemes of points on a surface. https://arxiv.org/abs/1407.5490

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