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April 2021 Of limit key polynomials
Maria Alberich-Carramiñana, Alberto F. F. Boix, Julio Fernández, Jordi Guàrdia, Enric Nart, Joaquim Roé
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Illinois J. Math. 65(1): 201-229 (April 2021). DOI: 10.1215/00192082-8827671

Abstract

Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane–Vaquié key polynomials for valuations μν and abstract key polynomials for ν. Also, some results on invariants associated to limit key polynomials are obtained. In particular, if char(K)=0, we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.

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Maria Alberich-Carramiñana. Alberto F. F. Boix. Julio Fernández. Jordi Guàrdia. Enric Nart. Joaquim Roé. "Of limit key polynomials." Illinois J. Math. 65 (1) 201 - 229, April 2021. https://doi.org/10.1215/00192082-8827671

Information

Received: 18 May 2020; Revised: 18 September 2020; Published: April 2021
First available in Project Euclid: 24 December 2020

Digital Object Identifier: 10.1215/00192082-8827671

Subjects:
Primary: 13A18
Secondary: 12J20 , 13J10 , 14E15

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 1 • April 2021
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