# The geometry of degenerations of Hilbert schemes of points

@article{Gulbrandsen2018TheGO, title={The geometry of degenerations of Hilbert schemes of points}, author={Martin G. Gulbrandsen and Lars Halvard Halle and Klaus Hulek and Ziyu Zhang}, journal={arXiv: Algebraic Geometry}, year={2018} }

Given a strict simple degeneration $f \colon X\to C$ the first three authors previously constructed a degeneration $I^n_{X/C} \to C$ of the relative degree $n$ Hilbert scheme of $0$-dimensional subschemes. In this paper we investigate the geometry of this degeneration, in particular when the fibre dimension of $f$ is at most $2$. In this case we show that $I^n_{X/C} \to C$ is a dlt model. This is even a good minimal dlt model if $f \colon X \to C$ has this property. We compute the dual complex… Expand

#### 3 Citations

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