Relative VGIT and an application to degenerations of Hilbert schemes

authored by

Lars H. Halle, Klaus Hulek, Ziyu Zhang

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].

Organisation(s)

Institut für Algebraische Geometrie

External Organisation(s)

University of Copenhagen
University of Shanghai for Science and Technology

Type

Artikel

Journal

Michigan mathematical journal

Volume

73

Pages

67 - 96

No. of pages

30

ISSN

0026-2285

Publication date

03.2023

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://arxiv.org/abs/1909.03780 (Access: Offen)
https://doi.org/10.1307/mmj/20205898 (Access: Geschlossen)