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arXiv · 2211.14368

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

Alberto Castaño Domínguez·Luis Narváez Macarro
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Abstract

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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Alberto Castaño Domínguez, Luis Narváez Macarro. 2023-08-18. On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities. https://doi.org/10.1007/s13163-023-00478-x

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