Multiple poles at negative integers for \({\int_A}f^\lambda\square\) in the case of an almost isolated singularity
type: Item
instance of: scholarly article
title: Multiple poles at negative integers for \({\int_A}f^\lambda\square\) in the case of an almost isolated singularity
zbMATH Open document ID: 0980.32012
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2001-02-06T00:00:00Z
review text: Let \(f: ({\mathbb R}^{n+1},0) \to ({\mathbb R},0)\) be a real analytic germ, and \(A\in H^0(\{f\neq 0\},{\mathbb C})\) a complex linear combination of connected components of \(\{f\neq 0\}\). The aim of the paper is to give a necessary and sufficient topological condition in order that the meromorphic extension of the holomorphic current \(\lambda \to \int_A f^\lambda\square\) has a multiple pole at sufficiently ``large'' negative integers. This is achieved under the assumption that the complexification \(f_{\mathbb C}: ({\mathbb C}^{n+1},0) \to ({\mathbb C},0)\) has an isolated singularity for the eigenvalue 1, i.e. the monodromy of \(f\) in nearby points does not have 1 as eigenvalue (on reduced cohomology of the local Milnor fibre).
reviewed by: Jan Stevens
Mathematics Subject Classification ID: 32S40
Mathematics Subject Classification ID: 14P15
zbMATH DE Number: 1437021
author: Daniel Barlet
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195143493
OpenAlex ID: W2247485958
cites work: Interaction de strates consécutives pour les cycles évanescents
cites work: Q4359305
cites work: Poles of \(\int_Af^s\bullet\) for an almost isolated singularity
cites work: Q3681128
DOI: 10.2977/PRIMS/1195143493
description: scientific article; zbMATH DE number 1437021