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arXiv · 2407.08293

Generating sequences of rank 1 valuations

Olga Kashcheyeva
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Abstract

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.

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Olga Kashcheyeva. 2024-07-11. Generating sequences of rank 1 valuations. https://arxiv.org/abs/2407.08293

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