Poincaré series of a rational surface singularity
type: Item
instance of: scholarly article
title: Poincaré series of a rational surface singularity
zbMATH Open document ID: 1060.14054
published in: Inventiones Mathematicae
publication date: 2004-07-07T00:00:00Z
review text: In this paper, \((S,0)\) is a germ of an isolated rational surface singularity and \(\pi:(X,D)\to (S,0)\) its minimal resolution. Here, \(X\) is a smooth surface, \(\pi\) is a proper analytic map which is an isomorphism outside of \(D=\pi^{-1} (0)\), the exceptional devisor \(D\) is the union of irreducible components \(E_i\) \((i=1,\dots,r)\) transversal to each other, each component \(E_i\) is isomorphic to the projective line \(\mathbb{C}\mathbb{P}^1\). Furthermore, we will see several definitions, key-words and notations. But we have no space to introduce these definitions in this review. The authors make and prove four important calculation theorems and two propositions. At the last page of this paper, the authors apply their theorems to the \(A_k\) surface singularity and the \(D_4\) surface singularity.
reviewed by: S. Ohyanagi
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 2078249
zbMATH Keywords: normal surface singularity
zbMATH Keywords: rational singularity
zbMATH Keywords: minimal resolution
author: Antonio Campillo
author: F. Delgado
author: Sabir M. Gusein-Zade
MaRDI profile type: Publication
full work available at URL: s00222-003-0310-y
OpenAlex ID: W2065627614
cites work: The Alexander polynomial of plane curve singularities and rings of functions on curves
cites work: The Alexander polynomial of a plane curve singularity via the ring of functions on it
cites work: Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity
cites work: Gorenstein property and symmetry for one-dimensional local Cohen-Macaulay rings
cites work: Germs of arcs on singular algebraic varieties and motivic integration
cites work: Q4204255
DOI: 10.1007/S00222-003-0310-Y
description: scientific article; zbMATH DE number 2078249