On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities

Given two holomorphic functions f and g defined in two respective germs of complex analytic manifolds (X, x) and (Y, y), we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum f+g can be expressed...

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Detalhes bibliográficos
Autores: Castaño Domínguez, Alberto, Narváez Macarro, Luis
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2024
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/157450
Acesso em linha:https://hdl.handle.net/11441/157450
https://doi.org/10.1007/s13163-023-00478-x
Access Level:Acceso aberto
Palavra-chave:Bernstein-Sato polynomial
Functional equation
Thom-Sebastiani singularity
V-filtration
Descrição
Resumo:Given two holomorphic functions f and g defined in two respective germs of complex analytic manifolds (X, x) and (Y, y), we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum f+g can be expressed in terms of those of f and g. In this note we give a purely algebraic proof of a similar relation between the whole functional equations that can be applied to any setting (not necessarily analytic) in which Bernstein-Sato polynomials can be defined.