A GIT construction of degenerations of Hilbert schemes of points

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

A GIT construction of degenerations of Hilbert schemes of points. / Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus.

I: Documenta Mathematica, Bind 24, 2019, s. 421-472.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Gulbrandsen, MG, Halle, LH & Hulek, K 2019, 'A GIT construction of degenerations of Hilbert schemes of points', Documenta Mathematica, bind 24, s. 421-472. https://doi.org/10.25537/dm.2019v24.421-472

APA

Gulbrandsen, M. G., Halle, L. H., & Hulek, K. (2019). A GIT construction of degenerations of Hilbert schemes of points. Documenta Mathematica, 24, 421-472. https://doi.org/10.25537/dm.2019v24.421-472

Vancouver

Gulbrandsen MG, Halle LH, Hulek K. A GIT construction of degenerations of Hilbert schemes of points. Documenta Mathematica. 2019;24:421-472. https://doi.org/10.25537/dm.2019v24.421-472

Author

Gulbrandsen, Martin G. ; Halle, Lars Halvard ; Hulek, Klaus. / A GIT construction of degenerations of Hilbert schemes of points. I: Documenta Mathematica. 2019 ; Bind 24. s. 421-472.

Bibtex

@article{f9868679b18948ac8f606a71aebdc100,
title = "A GIT construction of degenerations of Hilbert schemes of points",
abstract = "We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu shows that our GIT stack and the stack they construct are isomorphic, as are the associated coarse moduli schemes. Our construction is sufficiently explicit to obtain good control over the geometry of the singular fibres. We illustrate this by giving a concrete description of degenerations of degree Hilbert schemes of a simple degeneration with two components.",
author = "Gulbrandsen, {Martin G.} and Halle, {Lars Halvard} and Klaus Hulek",
year = "2019",
doi = "10.25537/dm.2019v24.421-472",
language = "English",
volume = "24",
pages = "421--472",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",

}

RIS

TY - JOUR

T1 - A GIT construction of degenerations of Hilbert schemes of points

AU - Gulbrandsen, Martin G.

AU - Halle, Lars Halvard

AU - Hulek, Klaus

PY - 2019

Y1 - 2019

N2 - We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu shows that our GIT stack and the stack they construct are isomorphic, as are the associated coarse moduli schemes. Our construction is sufficiently explicit to obtain good control over the geometry of the singular fibres. We illustrate this by giving a concrete description of degenerations of degree Hilbert schemes of a simple degeneration with two components.

AB - We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu shows that our GIT stack and the stack they construct are isomorphic, as are the associated coarse moduli schemes. Our construction is sufficiently explicit to obtain good control over the geometry of the singular fibres. We illustrate this by giving a concrete description of degenerations of degree Hilbert schemes of a simple degeneration with two components.

U2 - 10.25537/dm.2019v24.421-472

DO - 10.25537/dm.2019v24.421-472

M3 - Journal article

VL - 24

SP - 421

EP - 472

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

ER -

ID: 189316485