Multi-variable Poincaré series associated with Newton diagrams

W. Ebeling and S. M. Gusein-Zade

Journal of Singularities
volume 1 (2010), 60-68

Received 10 June 2009. Received in revised form 26 January 2010.

DOI: 10.5427/jsing.2010.1d

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Abstract:

We define a multi-index filtration on the ring of germs of functions on a hypersurface singularity associated with its Newton diagram and compute the multivariable Poincaré series of this filtration in some cases.

Keywords:

Newton diagram, filtration, 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