Arc K-semistability is a very general property
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917992991817728 |
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| author | Dervan, Ruadhaí |
| author_facet | Dervan, Ruadhaí |
| contents | We prove that arc K-semistability is a very general property in flat families of polarised varieties, and prove a similar result for uniform arc K-stability. This can be used to produce the only current examples of smooth uniformly arc K-stable varieties which are not known to admit a constant scalar curvature Kähler metric. Our technique is to prove a general result stating that semistability of a pair in the sense of Paul is a Zariski open property, and to employ prior work with Reboulet relating arc K-semistability to semistability of an associated pair. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arc K-semistability is a very general property Dervan, Ruadhaí Algebraic Geometry Differential Geometry We prove that arc K-semistability is a very general property in flat families of polarised varieties, and prove a similar result for uniform arc K-stability. This can be used to produce the only current examples of smooth uniformly arc K-stable varieties which are not known to admit a constant scalar curvature Kähler metric. Our technique is to prove a general result stating that semistability of a pair in the sense of Paul is a Zariski open property, and to employ prior work with Reboulet relating arc K-semistability to semistability of an associated pair. |
| title | Arc K-semistability is a very general property |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2504.15195 |