2003/09/15 by W. Ebeling, Wolfgang Ebeling, Ebeling, W. +3
Mathematics · #14B05 #32S10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #math.AG #msc:14B05 #msc:32S10
paper · pdf · doi:10.48550/arxiv.math/0309243
arxiv created 2003/09/15 · openalex publication_date 2003/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper, the authors introduced a filtration on the ring \cal OV,0 of germs of functions on a germ (V,0) of a complex analytic variety defined by arcs on the singularity and called the arc filtration. The Poincaré series of this filtration were computed for simple surface singularities in the 3-space. Here they are computed for surface singularities from Arnold's lists including uni- and bimodular ones. The classification of the unimodular singularities by these Poincaré series turns out to be in accordance with their hierarchy defined by E. Brieskorn using the adjacency relations. Besides that we give a general formula for the Poincaré series of the arc filtration for isolated surface singularities which are stabilizations of plane curve ones.