Relative VGIT and an Application to Degenerations of Hilbert Schemes

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Relative VGIT and an Application to Degenerations of Hilbert Schemes. / Halle, Lars H.; Hulek, Klaus; Zhang, Ziyu.

In: Michigan Mathematical Journal, Vol. 73, No. 1, 2023, p. 67-96.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Halle, LH, Hulek, K & Zhang, Z 2023, 'Relative VGIT and an Application to Degenerations of Hilbert Schemes', Michigan Mathematical Journal, vol. 73, no. 1, pp. 67-96. https://doi.org/10.1307/MMJ/20205898

APA

Halle, L. H., Hulek, K., & Zhang, Z. (2023). Relative VGIT and an Application to Degenerations of Hilbert Schemes. Michigan Mathematical Journal, 73(1), 67-96. https://doi.org/10.1307/MMJ/20205898

Vancouver

Halle LH, Hulek K, Zhang Z. Relative VGIT and an Application to Degenerations of Hilbert Schemes. Michigan Mathematical Journal. 2023;73(1):67-96. https://doi.org/10.1307/MMJ/20205898

Author

Halle, Lars H. ; Hulek, Klaus ; Zhang, Ziyu. / Relative VGIT and an Application to Degenerations of Hilbert Schemes. In: Michigan Mathematical Journal. 2023 ; Vol. 73, No. 1. pp. 67-96.

Bibtex

@article{e564d918474f43099ca6873b43671a30,
title = "Relative VGIT and an Application to Degenerations of Hilbert Schemes",
abstract = "We generalize the classical semicontinuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism X → S over an affine base S. As an application to moduli problems, we consider degenerations of Hilbert schemes and give a conceptual interpretation of the (semi)stable loci of the degeneration families constructed in [GHH19].",
author = "Halle, {Lars H.} and Klaus Hulek and Ziyu Zhang",
note = "Publisher Copyright: {\textcopyright} 2023 University of Michigan. All rights reserved.",
year = "2023",
doi = "10.1307/MMJ/20205898",
language = "English",
volume = "73",
pages = "67--96",
journal = "Michigan Mathematical Journal",
issn = "0026-2285",
publisher = "University of Michigan Department of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Relative VGIT and an Application to Degenerations of Hilbert Schemes

AU - Halle, Lars H.

AU - Hulek, Klaus

AU - Zhang, Ziyu

N1 - Publisher Copyright: © 2023 University of Michigan. All rights reserved.

PY - 2023

Y1 - 2023

N2 - We generalize the classical semicontinuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism X → S over an affine base S. As an application to moduli problems, we consider degenerations of Hilbert schemes and give a conceptual interpretation of the (semi)stable loci of the degeneration families constructed in [GHH19].

AB - We generalize the classical semicontinuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism X → S over an affine base S. As an application to moduli problems, we consider degenerations of Hilbert schemes and give a conceptual interpretation of the (semi)stable loci of the degeneration families constructed in [GHH19].

UR - http://www.scopus.com/inward/record.url?scp=85152270284&partnerID=8YFLogxK

U2 - 10.1307/MMJ/20205898

DO - 10.1307/MMJ/20205898

M3 - Journal article

AN - SCOPUS:85152270284

VL - 73

SP - 67

EP - 96

JO - Michigan Mathematical Journal

JF - Michigan Mathematical Journal

SN - 0026-2285

IS - 1

ER -

ID: 359600959