On a Newton filtration for functions on a curve singularity
Journal of Singularities, Tome 4 (2012), pp. 180-187
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In a previous paper, there was defined a multi-index filtration on the ring of functions on a hypersurface singularity corresponding to its Newton diagram generalizing (for a curve singularity) the divisorial one. Its Poincaré series was computed for plane curve singularities non-degenerate with respect to their Newton diagrams. Here we use another technique to compute the Poincaré series for plane curve singularities without the assumption that they are non-degenerate with respect to their Newton diagrams. We show that the Poincaré series only depends on the Newton diagram and not on the defining equation.
@article{10_5427_jsing_2012_4k,
author = {W. Ebeling and S. M. Gusein-Zade},
title = {On a {Newton} filtration for functions on a curve singularity},
journal = {Journal of Singularities},
pages = {180--187},
publisher = {mathdoc},
volume = {4},
year = {2012},
doi = {10.5427/jsing.2012.4k},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.4k/}
}
TY - JOUR AU - W. Ebeling AU - S. M. Gusein-Zade TI - On a Newton filtration for functions on a curve singularity JO - Journal of Singularities PY - 2012 SP - 180 EP - 187 VL - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.4k/ DO - 10.5427/jsing.2012.4k ID - 10_5427_jsing_2012_4k ER -
W. Ebeling; S. M. Gusein-Zade. On a Newton filtration for functions on a curve singularity. Journal of Singularities, Tome 4 (2012), pp. 180-187. doi: 10.5427/jsing.2012.4k
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