Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 1

Gulbrandsen-Halle-Hulek degeneration and Hilbert-Chow morphism

Pages: 401 – 442

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n1.a11


Yasunari Nagai (Department of Mathematics, Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan)


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