On a Newton filtration for functions on a curve singularity

Wolfgang Ebeling; Sabir M. Gusein-Zade

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arXiv · 1206.0135

On a Newton filtration for functions on a curve singularity

Wolfgang Ebeling·Sabir M. Gusein-Zade

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Abstract

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.

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BibTeX RIS

Wolfgang Ebeling, Sabir M. Gusein-Zade. 2012-06-01. On a Newton filtration for functions on a curve singularity. https://arxiv.org/abs/1206.0135

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