Publication

Of limit key polynomials

Journal Article (2021)

Journal

Illinois Journal of Mathematics

Pages

201-229

Volume

65

Number

1

Doc link

http://dx.doi.org/10.1215/00192082-8827671

File

Download the digital copy of the doc pdf document

Authors

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 μ ≤ν 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.

Categories

pattern recognition.

Author keywords

Valuation; MacLane-Vaquié Key polynomial; Abstract key polynomial; augmentation

Scientific reference

M. Alberich-Carramiñana, A. Fernández-Boix, J. Fernández, J. Guàrdia, E. Nart and J. Roé. Of limit key polynomials. Illinois Journal of Mathematics, 65(1): 201-229, 2021.