For a semistable degeneration of surfaces without a triple point, we show that two models of degeneration of Hilbert scheme of points of the family, Gulbrandsen–Halle–Hulek degeneration given in [M. G. Gulbrandsen, L. H. Halle, and K. Hulek, “A GIT construction of degenerations of Hilbert schemes of points”, Doc. Math. 24 (2019), 421–472] and the one given by the author in [Y. Nagai, “Symmetric products of a semistable degeneration of surfaces”, Math. Z. 289 (2018), no. 3-4, 1143–1168], are actually isomorphic.

中文翻译：

---

Gulbrandsen-Halle-Hulek变性和Hilbert-Chow态射

对于没有三点的表面的半稳定退化，我们显示了两个家族的点的希尔伯特模式的退化模型，即[G Gulbrandsen，LH Halle和K.Hulek，“ A GIT”中给出的Gulbrandsen–Halle–Hulek退化。希尔伯特积分方案退化的构建”，Doc。数学。24（2019），421–472]和作者在[Y. Nagai，“表面的半稳定退化的对称乘积”，数学。Z. 289（2018），没有。3-4，1143–1168]，实际上是同构的。