Relative VGIT and an application to degenerations of Hilbert schemes
Algebraic Geometry
2021-12-09 v2
Abstract
We generalize the classical semi-continuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism from X to 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 by Gulbrandsen-Halle-Hulek.
Keywords
Cite
@article{arxiv.1909.03780,
title = {Relative VGIT and an application to degenerations of Hilbert schemes},
author = {Lars H. Halle and Klaus Hulek and Ziyu Zhang},
journal= {arXiv preprint arXiv:1909.03780},
year = {2021}
}
Comments
27 pages, major revision, final version, to appear in Michigan Math. J