On the symmetry of \(b\)-functions of linear free divisors
type: Item
instance of: scholarly article
title: On the symmetry of \(b\)-functions of linear free divisors
zbMATH Open document ID: 1202.14046
DOI: 10.2977/PRIMS/15
author: Michel Granger
author: Mathias Schulze
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2010-10-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/0807.0560
review text: The authors introduce the concept of a prehomogeneous determinant as a generalization for linear free divisors. They show that the \(b-\)function roots are symmetric about \(-1\) for reductive prehomogeneous determinants and for the regular special free divisor. As a consequence, they get a positive answer to a question raised by Castro-Jiménez and Ucha-Enriquez, saying that \(-1\) is the only integer root of the corresponding \(b-\)function. As an application, the authors obtain new cases when the logarithmic comparison theorem holds.
reviewed by: Alexandru Dimca
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 14F40
zbMATH DE Number: 5803089
zbMATH Keywords: linear free divisor
zbMATH Keywords: prehomogeneous vector space
zbMATH Keywords: b-function
describes a project that uses: Macaulay2
MaRDI profile type: Publication
arXiv ID: 0807.0560
cites work: The analytic continuation of generalized functions with respect to a parameter
cites work: Q3964695
cites work: Q5488911
cites work: Cohomology of the complement of a free divisor
cites work: Testing the Logarithmic Comparison Theorem for Free Divisors
cites work: Logarithmic cohomology of the complement of a plane curve
cites work: Q4786363
cites work: Duality and comparison for logarithmic de Rham complexes with respect to free divisors.
cites work: On the logarithmic comparison theorem for integrable logarithmic connections
cites work: Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières
cites work: Linear free divisors and Frobenius manifolds
cites work: On the De Rham Cohomology of a Hypersurface Complement
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description: scientific article