On some properties of the asymptotic Samuel function
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912395535843328 |
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| author | Bravo, A. Encinas, S. Guillán-Rial, J. |
| author_facet | Bravo, A. Encinas, S. Guillán-Rial, J. |
| contents | The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11489 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On some properties of the asymptotic Samuel function Bravo, A. Encinas, S. Guillán-Rial, J. Commutative Algebra 13B22, 13H15 The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions. |
| title | On some properties of the asymptotic Samuel function |
| topic | Commutative Algebra 13B22, 13H15 |
| url | https://arxiv.org/abs/2307.11489 |