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
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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].
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