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ON A BERNSTEIN–SATO POLYNOMIAL OF A MEROMORPHIC FUNCTION

Part of: (Co)homology theory Singularities Analytic spaces

Published online by Cambridge University Press:  06 June 2023

KIYOSHI TAKEUCHI Open the ORCID record for KIYOSHI TAKEUCHI [Opens in a new window]
KIYOSHI TAKEUCHI*
Affiliation:
Mathematical Institute Tohoku University Aramaki Aza-Aoba 6-3 Aobaku, Sendai 980-8578, Japan
*
takemicro@nifty.com
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Abstract

We define Bernstein–Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara–Malgrange-type theorem on their geometric monodromies, which would also be useful in relation with the monodromy conjecture. A new feature in the meromorphic setting is that we have several b-functions whose roots yield the same set of the eigenvalues of the Milnor monodromies. We also introduce multiplier ideal sheaves for meromorphic functions and show that their jumping numbers are related to our b-functions.

MSC classification

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
Secondary: 14F18: Multiplier ideals 32C38: Sheaves of differential operators and their modules, $D$-modules 32S40: Monodromy; relations with differential equations and $D$-modules

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Type
Article
Information
Nagoya Mathematical Journal , Volume 251 , September 2023 , pp. 715 - 733
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

To the memory of Professor Hikosaburo Komatsu

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