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arXiv · 2005.04406

Invariants of limit key polynomials

Maria Alberich-Carramiñana·Alberto F. Boix·Julio Fernández·Jordi Guàrdia·Enric Nart·Joaquim Roé
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Abstract

Let $\nu$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with coefficients in a field $K$. We prove comparison theorems between MacLane-Vaqui\'e key polynomials for valuations $\mu\le\nu$ and abstract key polynomials for $\nu$. Also, some results on invariants attached to limit key polynomials are obtained. In particular, if $\operatorname{char}(K)=0$ we show that all limit key polynomials of unbounded continuous MacLane chains have numerical character equal to one.

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Maria Alberich-Carramiñana, Alberto F. Boix, Julio Fernández, Jordi Guàrdia, Enric Nart, Joaquim Roé. 2020-05-09. Invariants of limit key polynomials. https://arxiv.org/abs/2005.04406

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