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].
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Michigan Mathematical Journal |
| Vol/bind | 73 |
| Udgave nummer | 1 |
| Sider (fra-til) | 67-96 |
| ISSN | 0026-2285 |
| DOI | |
| Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:The authors would like to thank Alexander H.W. Schmitt for pointing out the reference [Sch08]. Klaus Hulek would like to thank Sándor Kovács, Thomas Peternell, and Charles Vial for discussions on higher-dimensional birational geometry and algebraic cycles. We are also grateful to the anonymous referee for several suggestions for improving the presentation of the paper and, in particular, for pointing out to us the reference [CJL14].
Publisher Copyright:
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