Generalization of Gurjar's Hyperplane section theorem to arbitrary analytic varieties and A$\mathbb{m}$AC classes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910344397455360 |
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| author | Parameswaran, A. J. Upmanyu, Mohit |
| author_facet | Parameswaran, A. J. Upmanyu, Mohit |
| contents | The aim of this paper is to generalize the hyperplane section theorem of Gurjar to arbitrary (local) analytic varieties even if the intersection with of hyperplanes is not necessarily isolated.
In case of formal varieties, we generalize the statement to work for different classes of functions than just hyperplanes. We call these classes (which are subsets of formal power series ring) to be algebraic $\mathbb{m}$-adicaly closed (A$\mathbb{m}$AC). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05594 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generalization of Gurjar's Hyperplane section theorem to arbitrary analytic varieties and A$\mathbb{m}$AC classes Parameswaran, A. J. Upmanyu, Mohit Algebraic Geometry Commutative Algebra The aim of this paper is to generalize the hyperplane section theorem of Gurjar to arbitrary (local) analytic varieties even if the intersection with of hyperplanes is not necessarily isolated. In case of formal varieties, we generalize the statement to work for different classes of functions than just hyperplanes. We call these classes (which are subsets of formal power series ring) to be algebraic $\mathbb{m}$-adicaly closed (A$\mathbb{m}$AC). |
| title | Generalization of Gurjar's Hyperplane section theorem to arbitrary analytic varieties and A$\mathbb{m}$AC classes |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2204.05594 |