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arXiv · 2509.17139

Optimal Parametrizations and Valuations

Reinhold Hübl·Craig Huneke·Sarasij Maitra·Vivek Mukundan
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Abstract

This article discusses a way for uniquely setting up the valuations for the minimal generators of the maximal ideal of a one dimensional complete reduced and irreducible local algebra over an algebraically closed field, when treated as a subring of its integral closure. Our observations are a generalization of the more well-studied case of a numerical semigroup ring. These results provide completion to some missing arguments in certain proofs present in the existing literature, including some results concerning a long-standing conjecture of R. Berger.

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Reinhold Hübl, Craig Huneke, Sarasij Maitra, Vivek Mukundan. 2025-09-21. Optimal Parametrizations and Valuations. https://arxiv.org/abs/2509.17139

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