Poincaré series of curves on rational surface singularities
type: Item
instance of: scholarly article
title: Poincaré series of curves on rational surface singularities
zbMATH Open document ID: 1075.14024
DOI: 10.4171/CMH/6
published in: Commentarii Mathematici Helvetici
publication date: 2005-04-18T00:00:00Z
review text: Let \((C,0)\) be a reducible curve singularity, embedded into a rational surface singularity \(({\mathcal S},0)\). The Poincaré series of \(C\) is defined by the multi-index filtration on the local ring defined by orders of a function on the branches of the curve. The aim of the paper is to compute the Poincaré series of \(C\). Special properties are pointed out for curves on \({\mathbb E_8}\), namely it is shown that the Poincaré series coincides with the Alexander polynomial (in several variables) of the corresponding link.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 32S25
zbMATH DE Number: 2157820
author: Antonio Campillo
author: F. Delgado
author: Sabir M. Gusein-Zade
reviewed by: Cristodor-Paul Ionescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2157820