Pure and Applied Mathematics Quarterly
Volume 17 (2021)
Gulbrandsen-Halle-Hulek degeneration and Hilbert-Chow morphism
Pages: 401 – 442
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.
Received 20 October 2020
Accepted 30 October 2020
Published 11 April 2021