On a Newton filtration for functions on a curve singularity

W. Ebeling and S. M. Gusein-Zade

Journal of Singularities
volume 4 (2012), 180-187

Received: 11 June 2012. Received in revised form: 14 November 2012.

DOI: 10.5427/jsing.2012.4k

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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.

Keywords:

filtrations, curve singularities, Newton diagrams, Poincaré series

Mathematical Subject Classification:

32S05, 14M25, 16W70

Author(s) information:

W. Ebeling	S. M. Gusein-Zade
Leibniz Universität Hannover	Moscow State University
Institut für Algebraische Geometrie, Postfach 6009	Faculty of Mechanics and Mathematics
D-30060 Hannover, Germany	Moscow, GSP-1, 119991, Russia
email: ebeling@math.uni-hannover.de	email: sabir@mccme.ru