On jet closures of singularities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913932255428608 |
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| author | Chen, Yifan Zuo, Huaiqing |
| author_facet | Chen, Yifan Zuo, Huaiqing |
| contents | The jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper, we introduce two local algebras associated to jet closure and jet support closure respectively. We show that these two algebras are invariants of the singularities. We compute and investigate these invariants for some interesting cases, such as the cases of monomial ideals and homogeneous ideals. We also introduce a new filtration and jet index to jet closures. The jet index describes which jet scheme recover the information of base scheme. Moreover, we obtain some properties of the jet index.
Keywords:jet closure, jet support closure and filtration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On jet closures of singularities Chen, Yifan Zuo, Huaiqing Commutative Algebra Algebraic Geometry 14B05 32S05 The jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper, we introduce two local algebras associated to jet closure and jet support closure respectively. We show that these two algebras are invariants of the singularities. We compute and investigate these invariants for some interesting cases, such as the cases of monomial ideals and homogeneous ideals. We also introduce a new filtration and jet index to jet closures. The jet index describes which jet scheme recover the information of base scheme. Moreover, we obtain some properties of the jet index. Keywords:jet closure, jet support closure and filtration. |
| title | On jet closures of singularities |
| topic | Commutative Algebra Algebraic Geometry 14B05 32S05 |
| url | https://arxiv.org/abs/2507.05796 |