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
Authors
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Alberich Carramiñana, Maria
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Fernández-Boix, Alberto
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Fernández, Julio
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Guàrdia, Jordi
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Nart, Enric
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Roé, Joaquim
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.
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