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...
| Autores: | , |
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| 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 |
| 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. |
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