Publications at the Riemann Center

The geometry of degenerations of Hilbert schemes of points

authored by
Martin G. Gulbrandsen, Lars H. Halle, Klaus Hulek, Ziyu Zhang
Abstract

Given a strict simple degeneration f : X → C the first three authors previously constructed a degeneration I

X/C

n → 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

X/C

n → C is a dlt model. This is even a good minimal dlt model if f : X → C has this property. We compute the dual complex of the central fibre (I

X/C

n )

0 and relate this to the essential skeleton of the generic fibre. For a type II degeneration of K3 surfaces we show that the stack I

X/C

n → C carries a nowhere degenerate relative logarithmic 2-form. Finally we discuss the relationship of our degeneration with the constructions of Nagai.

Organisation(s)
Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics
External Organisation(s)
University of Stavanger
University of Copenhagen
Type
Artikel
Journal
J ALGEBRAIC GEOM
Volume
30
Pages
1-56
No. of pages
56
ISSN
1056-3911
Publication date
2021
Publication status
Veröffentlicht
Peer reviewed
Yes
ASJC Scopus Sachgebiete
Geometrie und Topologie, Algebra und Zahlentheorie
Electronic version(s)
https://arxiv.org/abs/1802.00622 (Access: Offen)
https://doi.org/10.1090/jag/765 (Access: Geschlossen)