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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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.


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