The right classification of univariate power series in positive characteristic
Journal of Singularities, Tome 10 (2014), pp. 235-249
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While the classification of univariate power series up to coordinate change is trivial in characteristic 0, this classification is very different in positive characteristic. In this note we give a complete classification of univariate power series in K[[x]], where K is an algebraically closed field of characteristic p>0 by explicit normal forms. We show that the right determinacy of f is completely determined by its support. Moreover we prove that the right modality of f is equal to the integer part of \mu/p, where \mu is the Milnor number of f. As a consequence we prove in this case that the modality is equal to the proper modality, which is the dimension of the \mu-constant stratum in an algebraic representative of the semiuniversal deformation with trivial section.
@article{10_5427_jsing_2014_10p,
author = {Nguyen Hong Duc},
title = {The right classification of univariate power series in positive characteristic},
journal = {Journal of Singularities},
pages = {235--249},
publisher = {mathdoc},
volume = {10},
year = {2014},
doi = {10.5427/jsing.2014.10p},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.10p/}
}
TY - JOUR AU - Nguyen Hong Duc TI - The right classification of univariate power series in positive characteristic JO - Journal of Singularities PY - 2014 SP - 235 EP - 249 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.10p/ DO - 10.5427/jsing.2014.10p ID - 10_5427_jsing_2014_10p ER -
Nguyen Hong Duc. The right classification of univariate power series in positive characteristic. Journal of Singularities, Tome 10 (2014), pp. 235-249. doi: 10.5427/jsing.2014.10p
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