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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.08293 |
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| _version_ | 1866929417658302464 |
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| author | Kashcheyeva, Olga |
| author_facet | Kashcheyeva, Olga |
| contents | We consider a rank 1 valuation $ν$ centered in a regular 3-dimensional local ring $R$. We assume that the residue field $k$ of $ν$ is contained in $R$. An algorithm for constructing a generating sequences for $ν$ in $R$ is provided. This is a generalization of our previous algorithm where only valuations of rational rank 1 were considered. We then give a comparison example of a rational rank 3 valuation centered in a ring of polynomials in three variables for which we explicitly compute a set of key polynomials and a generating sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating sequences of rank 1 valuations Kashcheyeva, Olga Commutative Algebra We consider a rank 1 valuation $ν$ centered in a regular 3-dimensional local ring $R$. We assume that the residue field $k$ of $ν$ is contained in $R$. An algorithm for constructing a generating sequences for $ν$ in $R$ is provided. This is a generalization of our previous algorithm where only valuations of rational rank 1 were considered. We then give a comparison example of a rational rank 3 valuation centered in a ring of polynomials in three variables for which we explicitly compute a set of key polynomials and a generating sequence. |
| title | Generating sequences of rank 1 valuations |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2407.08293 |