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 L. H. Halle and K. 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

References

SHOWING 1-10 OF 43 REFERENCES
The essential skeleton of a degeneration of algebraic varieties
The essential skeleton of a product of degenerations
A relative Hilbert–Mumford criterion
The Homotopy Type of the Symmetric Products of Bouquets of Circles
The quantization conjecture revisited
A GIT construction of degenerations of Hilbert schemes of points
On the topology of cyclic products of spheres
Stable Morphisms to Singular Schemes and Relative Stable Morphisms
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